3731 + Interview Questions in Physics Page 48 InterviewSolution

2351.	A particle is projected from the ground at t = 0 so that on its way it just clears two vertical walls of equal height on the ground. If the particle passes just grazing top of the wall at time t1 and t2 then calculatethe height of the wall
Answer» A particle is projected from the ground at t = 0 so that on its way it just clears two vertical walls of equal height on the ground. If the particle passes just grazing top of the wall at time $t_{1} a n d t_{2}$ then calculate the height of the wall

2351.

A particle is projected from the ground at t = 0 so that on its way it just clears two vertical walls of equal height on the ground. If the particle passes just grazing top of the wall at time t1 and t2 then calculatethe height of the wall

Answer»

A particle is projected from the ground at t = 0 so that on its way it just clears two vertical walls of equal height on the ground. If the particle passes just grazing top of the wall at time $t_{1} a n d t_{2}$ then calculate

the height of the wall

Discussion

2352.	A ball hanging from a support by an inextensible string of length l is strucked perfectly inelastically by an identical ball of mass m moving with horizontal velocity of u=√2gl. Assuming the balls execute circular motion just after collision, find the tension in the string just after collision.
Answer» A ball hanging from a support by an inextensible string of length $l$ is strucked perfectly inelastically by an identical ball of mass $m$ moving with horizontal velocity of $u = \sqrt{2 g l}$ . Assuming the balls execute circular motion just after collision, find the tension in the string just after collision.

Discussion

2353.	In the situation shown in the figure, three lenses of focal lengths 20 cm, 30 cm and 36 cm are held coaxial such that separation between first and second lens is 12 cm and between second and third lens is 10 cm. If the final image of an object at a distance of 30 cm from first lens is at a distance 10x cm from the middle lens, then find the value of x.
Answer» In the situation shown in the figure, three lenses of focal lengths $20 cm, 30 cm$ and $36 cm$ are held coaxial such that separation between first and second lens is $12 cm$ and between second and third lens is $10 cm$ . If the final image of an object at a distance of $30 cm$ from first lens is at a distance $10 x cm$ from the middle lens, then find the value of $x$ .

Discussion

2354.	Figure below represents a Carnot engine that works between temperatures T1 400 K and T2 150 K and drives aCarnot refrigerator that works between temperatures T3 325 K and T4 225 K.What is the ratio Q3Q1?
Answer» Figure below represents a Carnot engine that works between temperatures $T_{1}$ 400 K and $T_{2}$ 150 K and drives aCarnot refrigerator that works between temperatures $T_{3}$ 325 K and $T_{4}$ 225 K.What is the ratio $\frac{Q 3}{Q 1}$ ?

2354.

Figure below represents a Carnot engine that works between temperatures T1 400 K and T2 150 K and drives aCarnot refrigerator that works between temperatures T3 325 K and T4 225 K.What is the ratio Q3Q1?

Answer»

Figure below represents a Carnot engine that works between temperatures $T_{1}$ 400 K and $T_{2}$ 150 K and drives aCarnot refrigerator that works between temperatures $T_{3}$ 325 K and $T_{4}$ 225 K.What is the ratio $\frac{Q 3}{Q 1}$ ?

Discussion

2355.	If a particle moves from point P (2,3,5) to point Q (3,4,5). Its displacement vector be
Answer» If a particle moves from point P (2,3,5) to point Q (3,4,5). Its displacement vector be

Discussion

2356.	Two small objects are 15 m apart on the water surface of a lake. Each object pops up and down with a period of 4.5 second due to wave motion on water surface.When one object is at its highest point, the another one is at its lowest point. Consider that objects are always within a single cycle of wave, the speed of wave is(Assume transverse surface waves)
Answer» Two small objects are $15 m$ apart on the water surface of a lake. Each object pops up and down with a period of $4.5 second$ due to wave motion on water surface. When one object is at its highest point, the another one is at its lowest point. Consider that objects are always within a single cycle of wave, the speed of wave is (Assume transverse surface waves)

Discussion

2357.	A pendulum bob of mass 250 gm is raised to a height of 4 cm and then released. At the bottom-most position of its swing, an insect of mass 25 gm sits on the bob. Find the maximum height to which the combined mass will rise. [Take g=10 m/s2]
Answer» A pendulum bob of mass $250 gm$ is raised to a height of $4 cm$ and then released. At the bottom-most position of its swing, an insect of mass $25 gm$ sits on the bob. Find the maximum height to which the combined mass will rise. [Take $g = 10 {m/s}^{2}$ ]

Discussion

2358.	A ball is thrown upward from the top of a tower of height 50 m with a velocity of 15 m/s. Find the time when it strikes the ground. Take g=10 m/s2.
Answer» A ball is thrown upward from the top of a tower of height $50 m$ with a velocity of $15 m/s$ . Find the time when it strikes the ground. Take $g = 10 m / s^{2}$ .

Discussion

2359.	A spherical drop of capacitance1 μF is broken into eight drops of equal radius. Then, the capacitance of each small drop is ......
Answer» A spherical drop of capacitance $1 μ F$ is broken into eight drops of equal radius. Then, the capacitance of each small drop is ......

Discussion

2360.	A small metal sphere, carrying a net charge of q1=−2μC, is held in a stationery position by insulating supports. A second small metal sphere, with a net charge of q2=−8μC and mass 1.50g is projected towards q1. When the two spheres are 0.800m apart, q2 is moving towards q1 with speed 20 ms−1 as shown in the figure. Assume that the two spheres can be treated as point charges. You can ignore the force of gravity.The speed of q2 when the spheres are 0.400 m apart is
Answer» A small metal sphere, carrying a net charge of $q_{1} = - 2 μ C$ , is held in a stationery position by insulating supports. A second small metal sphere, with a net charge of $q_{2} = - 8 μ C$ and mass 1.50g is projected towards $q_{1}$ . When the two spheres are $0.800 m$ apart, $q_{2}$ is moving towards $q_{1}$ with speed $20 m s^{- 1}$ as shown in the figure. Assume that the two spheres can be treated as point charges. You can ignore the force of gravity. The speed of $q_{2}$ when the spheres are 0.400 m apart is

Discussion

2361.	A longitudinal sound wave given by p=5sinπ3(x−400t) (p is in N/m2, x is in metres and t is in seconds) is sent down a closed organ pipe. If the pipe vibrates in its second overtone, the length of the pipe is
Answer» A longitudinal sound wave given by $p = 5 sin \frac{π}{3} (x - 400 t)$ ( $p$ is in ${N/m}^{2}$ , $x$ is in metres and $t$ is in seconds) is sent down a closed organ pipe. If the pipe vibrates in its second overtone, the length of the pipe is

Discussion

2362.	In the following figure the masses of the blocks A and B are the same and each equal to m. The tensions in the strings OA and AB are T2 and T1 respectively. The system is in equilibrium with a constant horizontal force mg on B. Then T2 is:
Answer» In the following figure the masses of the blocks $A$ and $B$ are the same and each equal to $m$ . The tensions in the strings $O A$ and $A B$ are $T_{2}$ and $T_{1}$ respectively. The system is in equilibrium with a constant horizontal force $m g$ on $B$ . Then $T_{2}$ is:

Discussion

2363.	A guitar wire A vibrates at a fundamental frequency 600 Hz. A second identical wire B produces 6 beats per second with it when the tension in B is slightly less than that of A. Find the ratio of the tension in A to the tension in B.
Answer» A guitar wire $A$ vibrates at a fundamental frequency $600 Hz$ . A second identical wire $B$ produces $6$ beats per second with it when the tension in $B$ is slightly less than that of $A$ . Find the ratio of the tension in $A$ to the tension in $B$ .

Discussion

2364.	The amplitude, speed and frequency of a plane progressive wave are respectively 0.05 m,333 m/s, and 110 Hz. Write the equation of the wave.
Answer» The amplitude, speed and frequency of a plane progressive wave are respectively 0.05 m,333 m/s, and 110 Hz. Write the equation of the wave.

Discussion

2365.	Water is drawn from a well in a 5 kg drum of capacity 55 L by two ropes connected to the top of the drum. The linear mass density of each rope is 0.5 kgm−1. The work done in lifting water to the ground from the surface of water in the well 20 m below is [g = 10 ms−2]
Answer» Water is drawn from a well in a 5 kg drum of capacity 55 L by two ropes connected to the top of the drum. The linear mass density of each rope is 0.5 kg $m^{- 1}$ . The work done in lifting water to the ground from the surface of water in the well 20 m below is [g = 10 m $s^{- 2}$ ]

Discussion

2366.	A uniform cylinder has a radius R and length L. If the moment of inertia of this cylinder about an axis passing through its centre and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through its centre and normal to its length; then
Answer» A uniform cylinder has a radius $R$ and length $L$ . If the moment of inertia of this cylinder about an axis passing through its centre and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through its centre and normal to its length; then

Discussion

2367.	The refractive index of the material of a prism is √2 and the angle of the prism is 300. One of the two refracting surfaces of the prism is made a mirror facing inwards by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface), if its angle of incidence on the prism is
Answer» The refractive index of the material of a prism is $\sqrt{2}$ and the angle of the prism is $30^{0}$ . One of the two refracting surfaces of the prism is made a mirror facing inwards by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface), if its angle of incidence on the prism is

Discussion

2368.	Find the angle of deviation for the incident ray.
Answer» Find the angle of deviation for the incident ray.

Discussion

2369.	The density of a liquid of coefficient of cubical expansion γ is ρ at 0∘C. When the liquid is heated to a temperature T, the change in density will be
Answer» The density of a liquid of coefficient of cubical expansion $γ$ is $ρ$ at $0^{\circ} C$ . When the liquid is heated to a temperature T, the change in density will be

Discussion

2370.	While light is used to illuminate the two slits in Young's double slit experiment. The separation between the slits is d and the distance between the screen and the slit is D (>> d). At a point on the screen directly in front of one of the slits, certain wavelengths are missing. The missing wavelengths are (here m=0, 1, 2, .....is an integer)
Answer» While light is used to illuminate the two slits in Young's double slit experiment. The separation between the slits is d and the distance between the screen and the slit is D (>> d). At a point on the screen directly in front of one of the slits, certain wavelengths are missing. The missing wavelengths are (here m=0, 1, 2, .....is an integer)

Discussion

2371.	If a capillary tube is dipped into liquid and the level of the liquid inside and outside are same, then the angle of contact is
Answer» If a capillary tube is dipped into liquid and the level of the liquid inside and outside are same, then the angle of contact is

Discussion

2372.	A body starts from rest and is uniformly accelerated for 30 s. The distance travelled in the first 10 s is x1, next 10 s is x2 and the last 10 s is x3. Then x1:x2:x3 is the same as
Answer» A body starts from rest and is uniformly accelerated for $30 s$ . The distance travelled in the first $10 s$ is $x_{1}$ , next $10 s$ is $x_{2}$ and the last $10 s$ is $x_{3}$ . Then $x_{1} : x_{2} : x_{3}$ is the same as

Discussion

2373.	A hollow cylindrical pipe of length 10 cm has inner radius r1=3 cm and outer radius r2=12 cm. The temperature difference between the inner and outer layer of cylindrical pipe is 100∘C and the thermal conductivity of cylindrical pipe is 150 W/m∘C. Find the rate of heat transfered (in kW) between inner and outer layers.(Take ln2=0.693)
Answer» A hollow cylindrical pipe of length $10 cm$ has inner radius $r_{1} = 3 cm$ and outer radius $r_{2} = 12 cm$ . The temperature difference between the inner and outer layer of cylindrical pipe is $100^{\circ} C$ and the thermal conductivity of cylindrical pipe is $150 {W/m}^{\circ} C$ . Find the rate of heat transfered (in $kW$ ) between inner and outer layers. (Take $ln 2 = 0.693$ )

Discussion

2374.	Assume the gas to be ideal, the work done on the gas in taking it from A to B is
Answer» Assume the gas to be ideal, the work done on the gas in taking it from A to B is

Discussion

2375.	The current ‘i′ in an inductance coil varies with time ‘t′ according to the following graphWhich one of the following plots shows the variations of voltage in the coil magnitude wise? (all vertical lines are not part of graphs)
Answer» The current $‘ i^{'}$ in an inductance coil varies with time $‘ t^{'}$ according to the following graph Which one of the following plots shows the variations of voltage in the coil magnitude wise? (all vertical lines are not part of graphs)

Discussion

2376.	A rectangular loop ABCD is being pulled out of a magnetic field ′B′ with uniform velocity ′v′ by applying an external force F. Length AB is l. Length AD is 3l and total resistance of the loop is R. The thermal power developed in the loop and the force F respectively is
Answer» A rectangular loop $A B C D$ is being pulled out of a magnetic field $^{'} B^{'}$ with uniform velocity $^{'} v^{'}$ by applying an external force $F$ . Length $A B$ is $l$ . Length $A D$ is $3 l$ and total resistance of the loop is $R$ . The thermal power developed in the loop and the force $F$ respectively is

Discussion

2377.	When light falls on a metal surface, the maximum kinetic energy of the emitted photo-electrons depends upon
Answer» When light falls on a metal surface, the maximum kinetic energy of the emitted photo-electrons depends upon

Discussion

2378.	The initial velocity of a body moving along a straight line is 7 m/s. It has a uniform acceleration of 4 m/s2. The distance covered by the body in the 5th second of its motion is
Answer» The initial velocity of a body moving along a straight line is $7 m/s$ . It has a uniform acceleration of $4 {m/s}^{2}$ . The distance covered by the body in the $5^{th}$ second of its motion is

Discussion

2379.	A knife of mass m is at a height x from a large wooden block. The knife is allowed to fall freely, strikes the block and comes to rest after penetrating distance y. The work done by the wooden block to stop the knife is
Answer» A knife of mass $m$ is at a height $x$ from a large wooden block. The knife is allowed to fall freely, strikes the block and comes to rest after penetrating distance $y$ . The work done by the wooden block to stop the knife is

Discussion

2380.	If →r.^i=→r.^j=→r.^k and \|→r\|=3, then →r is equal to
Answer» If $\to r .^i = \to r .^j = \to r .^k and \| \to r \| = 3, then \to r$ is equal to

Discussion

2381.	A particle starts from x=0 and moves along a straight line such that its velocity v depends on position x as v=x+4. For the first four seconds, average velocity of the particle (in m/s) is
Answer» A particle starts from $x = 0$ and moves along a straight line such that its velocity $v$ depends on position $x$ as $v = x + 4$ . For the first four seconds, average velocity of the particle (in $m / s$ ) is

Discussion

2382.	A liquid of mass m and specific heat c is heated to a temperature 2T. Another liquid of mass m/2 and specific heat 2c is heated to a temperature T. If these two liquids are mixed, the resulting temperature of the mixture is
Answer» A liquid of mass m and specific heat c is heated to a temperature 2T. Another liquid of mass m/2 and specific heat 2c is heated to a temperature T. If these two liquids are mixed, the resulting temperature of the mixture is

Discussion

2383.	A ball of mass 100 g is projected with a velocity of 50 m/s at 37∘ from horizontal. Using the concept of impulse, find the magnitude of change in velocity of ball in 2 s (Take g = 10 m/s2)
Answer» A ball of mass $100 g$ is projected with a velocity of $50 m/s$ at $37^{\circ}$ from horizontal. Using the concept of impulse, find the magnitude of change in velocity of ball in $2 s$ (Take g = 10 m/s $^{2}$ )

Discussion

2384.	A wheel is making revolutions about its axis with uniform angular acceleration. Starting from rest, it reaches 100 rev/sec in 4 secs. Its angular acceleration is.
Answer» A wheel is making revolutions about its axis with uniform angular acceleration. Starting from rest, it reaches 100 rev/sec in 4 secs. Its angular acceleration is.

Discussion

2385.	A string of length L fixed at both ends vibrates in its fundamental node at a frequency v and a maximum amplitude A. Take the origin at one end of the string and the X-axis along the string. Take the Y-axis along the direction of the displacement. Take t = 0 at the instant when the middle point of the string passes through its mean position and is going towards the positive y-direction. Write the equation describing the standing wave.
Answer» A string of length L fixed at both ends vibrates in its fundamental node at a frequency v and a maximum amplitude A. Take the origin at one end of the string and the X-axis along the string. Take the Y-axis along the direction of the displacement. Take t = 0 at the instant when the middle point of the string passes through its mean position and is going towards the positive y-direction. Write the equation describing the standing wave.

Discussion

2386.	The wave length of Kα, x- rays produced by an x-ray tube is λ. The atomic number of the anode material of the tube is: (Constants have their usual meanings)
Answer» The wave length of $K_{α}$ , x- rays produced by an x-ray tube is $λ$ . The atomic number of the anode material of the tube is: (Constants have their usual meanings)

Discussion

2387.	A particle moves along a straight line. Its position at any instant is given by x=32t−8t33 where x is in m and t in s. The acceleration of the particle at the instant when particle is at rest will be
Answer» A particle moves along a straight line. Its position at any instant is given by $x = 32 t - \frac{8 t^{3}}{3}$ where $x$ is in $m$ and $t$ in $s$ . The acceleration of the particle at the instant when particle is at rest will be

Discussion

2388.	In the following four periods (i) Time of revolution of a satellite just above the earth’s surface (Tst)(ii) Period of oscillation of mass inside the tunnel bored along the diameter of the earth (Tma)(iii) Period of simple pendulum having a length equal to the earth’s radius in a uniform field of 9.8 N/k (Tsp)(iv) Period of an infinite length simple pendulum in the earth’s real gravitational field (Tis)
Answer» In the following four periods (i) Time of revolution of a satellite just above the earth’s surface $(T_{s t})$ (ii) Period of oscillation of mass inside the tunnel bored along the diameter of the earth $(T_{m a})$ (iii) Period of simple pendulum having a length equal to the earth’s radius in a uniform field of 9.8 N/k $(T_{s p})$ (iv) Period of an infinite length simple pendulum in the earth’s real gravitational field $(T_{i s})$

Discussion

2389.	Find the dimensions of the following quantities:(i) the surfaces tension S, (ii) the coefficient of viscosity η.Some equations involving these quantities areS=ρgrh2 and F=−ηAv2−v1x2−x1Where the symbol have their usual meanings.ρ is density g is acceleration r, h and x are lengthF is force, A is area.
Answer» Find the dimensions of the following quantities: (i) the surfaces tension S, (ii) the coefficient of viscosity $η$ . Some equations involving these quantities are $S = \frac{ρ g r h}{2}$ and $F = - η A \frac{v_{2} - v_{1}}{x_{2} - x_{1}}$ Where the symbol have their usual meanings. $ρ$ is density g is acceleration r, h and x are length F is force, A is area.

2389.

Find the dimensions of the following quantities:(i) the surfaces tension S, (ii) the coefficient of viscosity η.Some equations involving these quantities areS=ρgrh2 and F=−ηAv2−v1x2−x1Where the symbol have their usual meanings.ρ is density g is acceleration r, h and x are lengthF is force, A is area.

Answer»

Find the dimensions of the following quantities:

(i) the surfaces tension S, (ii) the coefficient of viscosity $η$ .

Some equations involving these quantities are

$S = \frac{ρ g r h}{2}$ and $F = - η A \frac{v_{2} - v_{1}}{x_{2} - x_{1}}$

Where the symbol have their usual meanings.

$ρ$ is density g is acceleration r, h and x are length

F is force, A is area.

Discussion

2390.	In a rectangle ABCD where A is origin as shown in the figure, what is −−→AB+−−→AD ?
Answer» In a rectangle $A B C D$ where $A$ is origin as shown in the figure, what is $- - \to A B + - - \to A D$ ?

Discussion

2391.	Two rotating bodies A and B of masses m and 2m with moments of inertia IA and IB (IB > IA) have equal kinetic energy of rotation. If LA and LB be their angular momenta respectively, then
Answer» Two rotating bodies A and B of masses $m$ and $2 m$ with moments of inertia $I_{A}$ and $I_{B}$ ( $I_{B}$ > $I_{A}$ ) have equal kinetic energy of rotation. If $L_{A}$ and $L_{B}$ be their angular momenta respectively, then

Discussion

2392.	The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by y=(4t−2t2) m and x=(3t) m, where t is in seconds and point of projection is taken as origin. The angle of projection of projectile with vertical is
Answer» The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by $y = (4 t - 2 t^{2}) m$ and $x = (3 t) m$ , where $t$ is in seconds and point of projection is taken as origin. The angle of projection of projectile with vertical is

Discussion

2393.	An object moving with an speed of 25 m/s is decelerating at a rate give by a=−5√v , where, v is speed at any time. The time taken by the object to come at rest is
Answer» An object moving with an speed of $25 m/s$ is decelerating at a rate give by $a = - 5 \sqrt{v},$ where, $v$ is speed at any time. The time taken by the object to come at rest is

Discussion

2394.	If a thermometer reads freezing point of water as 20∘ and boiling point as 150∘, how much does the thermometer read when the actual temperature is 60∘C?
Answer» If a thermometer reads freezing point of water as $20^{\circ}$ and boiling point as $150^{\circ}$ , how much does the thermometer read when the actual temperature is $60^{\circ} C$ ?

Discussion

2395.	A regular hexagonal uniform block of mass m=4√3 kg rests on a rough horizontal surface with coefficient of friction μ as shown in figure. A constant horizontal force is applied on the block as shown. If the friction is sufficient to prevent slipping before toppling, then the minimum force (in N) required to topple the block about its corner A is (Take g=10 m/s2)
Answer» A regular hexagonal uniform block of mass $m = 4 \sqrt{3} kg$ rests on a rough horizontal surface with coefficient of friction $μ$ as shown in figure. A constant horizontal force is applied on the block as shown. If the friction is sufficient to prevent slipping before toppling, then the minimum force (in $N$ ) required to topple the block about its corner $A$ is (Take $g = 10 {m/s}^{2}$ )

Discussion

2396.	A test tube of cross-sectional area a has some lead shots in it. The total mass is m. It floats upright in liquid of density d. when pushed down little and released, it oscillates up and down with a period T. Use dimensional considerations and choose the correct relationship from the following.
Answer» A test tube of cross-sectional area a has some lead shots in it. The total mass is m. It floats upright in liquid of density d. when pushed down little and released, it oscillates up and down with a period T. Use dimensional considerations and choose the correct relationship from the following.

Discussion

2397.	The translational kinetic energy of all the molecules of 1 mole of Helium gas having a volume V exerting a pressure P is 1000 J. The total kinetic energy (in Joule) of all the molecules of 1 mole of N2 gas having the same volume V and exerting a pressure 2P is :
Answer» The translational kinetic energy of all the molecules of $1$ mole of Helium gas having a volume $V$ exerting a pressure $P$ is $1000 J$ . The total kinetic energy (in $Joule$ ) of all the molecules of $1$ mole of $N_{2}$ gas having the same volume $V$ and exerting a pressure $2 P$ is :

Discussion

2398.	The figure shows a solenoid carrying time varying current I=I0t. On the axis of this solenoid a ring has been placed. The mutual inductance of the ring and the solenoid is M and the self inductance of the ring is L. If the resistance of the ring is R then the maximum current which can flow through the ring is equal to
Answer» The figure shows a solenoid carrying time varying current $I = I_{0} t$ . On the axis of this solenoid a ring has been placed. The mutual inductance of the ring and the solenoid is $M$ and the self inductance of the ring is $L$ . If the resistance of the ring is $R$ then the maximum current which can flow through the ring is equal to

Discussion

2399.	The coefficient of expansion of a crystal in one direction (x-axis) is 2.0×10−6 K−1 and that in the other two perpendicular directions (y and z-axes) is 1.6×10−6 K−1,What is the coefficient of cubical expansion of the crystal?
Answer» The coefficient of expansion of a crystal in one direction (x-axis) is $2.0 \times 10^{- 6} K^{- 1}$ and that in the other two perpendicular directions (y and z-axes) is $1.6 \times 10^{- 6} K^{- 1},$ What is the coefficient of cubical expansion of the crystal?

Discussion

2400.	Find the time period of small oscillations of the following systems.(p) A metre stick suspended through the 20 cm mark.(q) A ring of mass m and radius r suspended through a point on its periphery.(r) A uniform square plate of edge 'a' suspended through a corner.(s) A uniform disc of mass m and radius r suspended through a point r2 away from the centre.(i)2π√2√2a3g (ii) 1.51 sec (iii) 2π√3r3g (iv)T=2π√2Rg
Answer» Find the time period of small oscillations of the following systems. (p) A metre stick suspended through the 20 cm mark. (q) A ring of mass m and radius r suspended through a point on its periphery. (r) A uniform square plate of edge 'a' suspended through a corner. (s) A uniform disc of mass m and radius r suspended through a point $\frac{r}{2}$ away from the centre. (i) $2 π \sqrt{\frac{2 \sqrt{2} a}{3 g}}$ (ii) 1.51 sec (iii) $2 π \sqrt{\frac{3 r}{3 g}}$ (iv) $T = 2 π \sqrt{\frac{2 R}{g}}$

2400.

Find the time period of small oscillations of the following systems.(p) A metre stick suspended through the 20 cm mark.(q) A ring of mass m and radius r suspended through a point on its periphery.(r) A uniform square plate of edge 'a' suspended through a corner.(s) A uniform disc of mass m and radius r suspended through a point r2 away from the centre.(i)2π√2√2a3g (ii) 1.51 sec (iii) 2π√3r3g (iv)T=2π√2Rg

Answer»

Find the time period of small oscillations of the following systems.

(p) A metre stick suspended through the 20 cm mark.

(q) A ring of mass m and radius r suspended through a point on its periphery.

(r) A uniform square plate of edge 'a' suspended through a corner.

(s) A uniform disc of mass m and radius r suspended through a point $\frac{r}{2}$ away from the centre.

(i) $2 π \sqrt{\frac{2 \sqrt{2} a}{3 g}}$ (ii) 1.51 sec (iii) $2 π \sqrt{\frac{3 r}{3 g}}$ (iv) $T = 2 π \sqrt{\frac{2 R}{g}}$

Discussion

Explore topic-wise InterviewSolutions in .

A particle is projected from the ground at t = 0 so that on its way it just clears two vertical walls of equal height on the ground. If the particle passes just grazing top of the wall at time t1 and t2 then calculatethe height of the wall

A ball hanging from a support by an inextensible string of length l is strucked perfectly inelastically by an identical ball of mass m moving with horizontal velocity of u=√2gl. Assuming the balls execute circular motion just after collision, find the tension in the string just after collision.

Figure below represents a Carnot engine that works between temperatures T1 400 K and T2 150 K and drives aCarnot refrigerator that works between temperatures T3 325 K and T4 225 K.What is the ratio Q3Q1?

If a particle moves from point P (2,3,5) to point Q (3,4,5). Its displacement vector be

A pendulum bob of mass 250 gm is raised to a height of 4 cm and then released. At the bottom-most position of its swing, an insect of mass 25 gm sits on the bob. Find the maximum height to which the combined mass will rise. [Take g=10 m/s2]

A ball is thrown upward from the top of a tower of height 50 m with a velocity of 15 m/s. Find the time when it strikes the ground. Take g=10 m/s2.

A spherical drop of capacitance1 μF is broken into eight drops of equal radius. Then, the capacitance of each small drop is ......

A longitudinal sound wave given by p=5sinπ3(x−400t) (p is in N/m2, x is in metres and t is in seconds) is sent down a closed organ pipe. If the pipe vibrates in its second overtone, the length of the pipe is

In the following figure the masses of the blocks A and B are the same and each equal to m. The tensions in the strings OA and AB are T2 and T1 respectively. The system is in equilibrium with a constant horizontal force mg on B. Then T2 is:

A guitar wire A vibrates at a fundamental frequency 600 Hz. A second identical wire B produces 6 beats per second with it when the tension in B is slightly less than that of A. Find the ratio of the tension in A to the tension in B.

The amplitude, speed and frequency of a plane progressive wave are respectively 0.05 m,333 m/s, and 110 Hz. Write the equation of the wave.

Water is drawn from a well in a 5 kg drum of capacity 55 L by two ropes connected to the top of the drum. The linear mass density of each rope is 0.5 kgm−1. The work done in lifting water to the ground from the surface of water in the well 20 m below is [g = 10 ms−2]

A uniform cylinder has a radius R and length L. If the moment of inertia of this cylinder about an axis passing through its centre and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through its centre and normal to its length; then

Find the angle of deviation for the incident ray.

The density of a liquid of coefficient of cubical expansion γ is ρ at 0∘C. When the liquid is heated to a temperature T, the change in density will be

If a capillary tube is dipped into liquid and the level of the liquid inside and outside are same, then the angle of contact is

A body starts from rest and is uniformly accelerated for 30 s. The distance travelled in the first 10 s is x1, next 10 s is x2 and the last 10 s is x3. Then x1:x2:x3 is the same as

Assume the gas to be ideal, the work done on the gas in taking it from A to B is

The current ‘i′ in an inductance coil varies with time ‘t′ according to the following graphWhich one of the following plots shows the variations of voltage in the coil magnitude wise? (all vertical lines are not part of graphs)

A rectangular loop ABCD is being pulled out of a magnetic field ′B′ with uniform velocity ′v′ by applying an external force F. Length AB is l. Length AD is 3l and total resistance of the loop is R. The thermal power developed in the loop and the force F respectively is

When light falls on a metal surface, the maximum kinetic energy of the emitted photo-electrons depends upon

The initial velocity of a body moving along a straight line is 7 m/s. It has a uniform acceleration of 4 m/s2. The distance covered by the body in the 5th second of its motion is

A knife of mass m is at a height x from a large wooden block. The knife is allowed to fall freely, strikes the block and comes to rest after penetrating distance y. The work done by the wooden block to stop the knife is

If →r.^i=→r.^j=→r.^k and |→r|=3, then →r is equal to

A particle starts from x=0 and moves along a straight line such that its velocity v depends on position x as v=x+4. For the first four seconds, average velocity of the particle (in m/s) is

A liquid of mass m and specific heat c is heated to a temperature 2T. Another liquid of mass m/2 and specific heat 2c is heated to a temperature T. If these two liquids are mixed, the resulting temperature of the mixture is

A ball of mass 100 g is projected with a velocity of 50 m/s at 37∘ from horizontal. Using the concept of impulse, find the magnitude of change in velocity of ball in 2 s (Take g = 10 m/s2)

A wheel is making revolutions about its axis with uniform angular acceleration. Starting from rest, it reaches 100 rev/sec in 4 secs. Its angular acceleration is.

The wave length of Kα, x- rays produced by an x-ray tube is λ. The atomic number of the anode material of the tube is: (Constants have their usual meanings)

A particle moves along a straight line. Its position at any instant is given by x=32t−8t33 where x is in m and t in s. The acceleration of the particle at the instant when particle is at rest will be

In a rectangle ABCD where A is origin as shown in the figure, what is −−→AB+−−→AD ?

Two rotating bodies A and B of masses m and 2m with moments of inertia IA and IB (IB > IA) have equal kinetic energy of rotation. If LA and LB be their angular momenta respectively, then

The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by y=(4t−2t2) m and x=(3t) m, where t is in seconds and point of projection is taken as origin. The angle of projection of projectile with vertical is

An object moving with an speed of 25 m/s is decelerating at a rate give by a=−5√v , where, v is speed at any time. The time taken by the object to come at rest is

If a thermometer reads freezing point of water as 20∘ and boiling point as 150∘, how much does the thermometer read when the actual temperature is 60∘C?

A test tube of cross-sectional area a has some lead shots in it. The total mass is m. It floats upright in liquid of density d. when pushed down little and released, it oscillates up and down with a period T. Use dimensional considerations and choose the correct relationship from the following.

The translational kinetic energy of all the molecules of 1 mole of Helium gas having a volume V exerting a pressure P is 1000 J. The total kinetic energy (in Joule) of all the molecules of 1 mole of N2 gas having the same volume V and exerting a pressure 2P is :

The coefficient of expansion of a crystal in one direction (x-axis) is 2.0×10−6 K−1 and that in the other two perpendicular directions (y and z-axes) is 1.6×10−6 K−1,What is the coefficient of cubical expansion of the crystal?

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A particle is projected from the ground at t = 0 so that on its way it just clears two vertical walls of equal height on the ground. If the particle passes just grazing top of the wall at time t1 and t2 then calculatethe height of the wall

A ball hanging from a support by an inextensible string of length l is strucked perfectly inelastically by an identical ball of mass m moving with horizontal velocity of u=√2gl. Assuming the balls execute circular motion just after collision, find the tension in the string just after collision.

Figure below represents a Carnot engine that works between temperatures T1 400 K and T2 150 K and drives aCarnot refrigerator that works between temperatures T3 325 K and T4 225 K.What is the ratio Q3Q1?

If a particle moves from point P (2,3,5) to point Q (3,4,5). Its displacement vector be

A pendulum bob of mass 250 gm is raised to a height of 4 cm and then released. At the bottom-most position of its swing, an insect of mass 25 gm sits on the bob. Find the maximum height to which the combined mass will rise. [Take g=10 m/s2]

A ball is thrown upward from the top of a tower of height 50 m with a velocity of 15 m/s. Find the time when it strikes the ground. Take g=10 m/s2.

A spherical drop of capacitance1 μF is broken into eight drops of equal radius. Then, the capacitance of each small drop is ......

A longitudinal sound wave given by p=5sinπ3(x−400t) (p is in N/m2, x is in metres and t is in seconds) is sent down a closed organ pipe. If the pipe vibrates in its second overtone, the length of the pipe is

In the following figure the masses of the blocks A and B are the same and each equal to m. The tensions in the strings OA and AB are T2 and T1 respectively. The system is in equilibrium with a constant horizontal force mg on B. Then T2 is:

A guitar wire A vibrates at a fundamental frequency 600 Hz. A second identical wire B produces 6 beats per second with it when the tension in B is slightly less than that of A. Find the ratio of the tension in A to the tension in B.

The amplitude, speed and frequency of a plane progressive wave are respectively 0.05 m,333 m/s, and 110 Hz. Write the equation of the wave.

Water is drawn from a well in a 5 kg drum of capacity 55 L by two ropes connected to the top of the drum. The linear mass density of each rope is 0.5 kgm−1. The work done in lifting water to the ground from the surface of water in the well 20 m below is [g = 10 ms−2]

A uniform cylinder has a radius R and length L. If the moment of inertia of this cylinder about an axis passing through its centre and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through its centre and normal to its length; then

Find the angle of deviation for the incident ray.

The density of a liquid of coefficient of cubical expansion γ is ρ at 0∘C. When the liquid is heated to a temperature T, the change in density will be

If a capillary tube is dipped into liquid and the level of the liquid inside and outside are same, then the angle of contact is

A body starts from rest and is uniformly accelerated for 30 s. The distance travelled in the first 10 s is x1, next 10 s is x2 and the last 10 s is x3. Then x1:x2:x3 is the same as

Assume the gas to be ideal, the work done on the gas in taking it from A to B is

The current ‘i′ in an inductance coil varies with time ‘t′ according to the following graphWhich one of the following plots shows the variations of voltage in the coil magnitude wise? (all vertical lines are not part of graphs)

A rectangular loop ABCD is being pulled out of a magnetic field ′B′ with uniform velocity ′v′ by applying an external force F. Length AB is l. Length AD is 3l and total resistance of the loop is R. The thermal power developed in the loop and the force F respectively is

When light falls on a metal surface, the maximum kinetic energy of the emitted photo-electrons depends upon

The initial velocity of a body moving along a straight line is 7 m/s. It has a uniform acceleration of 4 m/s2. The distance covered by the body in the 5th second of its motion is

A knife of mass m is at a height x from a large wooden block. The knife is allowed to fall freely, strikes the block and comes to rest after penetrating distance y. The work done by the wooden block to stop the knife is

If →r.^i=→r.^j=→r.^k and |→r|=3, then →r is equal to

A particle starts from x=0 and moves along a straight line such that its velocity v depends on position x as v=x+4. For the first four seconds, average velocity of the particle (in m/s) is

A liquid of mass m and specific heat c is heated to a temperature 2T. Another liquid of mass m/2 and specific heat 2c is heated to a temperature T. If these two liquids are mixed, the resulting temperature of the mixture is

A ball of mass 100 g is projected with a velocity of 50 m/s at 37∘ from horizontal. Using the concept of impulse, find the magnitude of change in velocity of ball in 2 s (Take g = 10 m/s2)

A wheel is making revolutions about its axis with uniform angular acceleration. Starting from rest, it reaches 100 rev/sec in 4 secs. Its angular acceleration is.

The wave length of Kα, x- rays produced by an x-ray tube is λ. The atomic number of the anode material of the tube is: (Constants have their usual meanings)

A particle moves along a straight line. Its position at any instant is given by x=32t−8t33 where x is in m and t in s. The acceleration of the particle at the instant when particle is at rest will be

In a rectangle ABCD where A is origin as shown in the figure, what is −−→AB+−−→AD ?

Two rotating bodies A and B of masses m and 2m with moments of inertia IA and IB (IB &gt; IA) have equal kinetic energy of rotation. If LA and LB be their angular momenta respectively, then

The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by y=(4t−2t2) m and x=(3t) m, where t is in seconds and point of projection is taken as origin. The angle of projection of projectile with vertical is

An object moving with an speed of 25 m/s is decelerating at a rate give by a=−5√v , where, v is speed at any time. The time taken by the object to come at rest is

If a thermometer reads freezing point of water as 20∘ and boiling point as 150∘, how much does the thermometer read when the actual temperature is 60∘C?

A test tube of cross-sectional area a has some lead shots in it. The total mass is m. It floats upright in liquid of density d. when pushed down little and released, it oscillates up and down with a period T. Use dimensional considerations and choose the correct relationship from the following.

The translational kinetic energy of all the molecules of 1 mole of Helium gas having a volume V exerting a pressure P is 1000 J. The total kinetic energy (in Joule) of all the molecules of 1 mole of N2 gas having the same volume V and exerting a pressure 2P is :

The coefficient of expansion of a crystal in one direction (x-axis) is 2.0×10−6 K−1 and that in the other two perpendicular directions (y and z-axes) is 1.6×10−6 K−1,What is the coefficient of cubical expansion of the crystal?

Two rotating bodies A and B of masses m and 2m with moments of inertia IA and IB (IB > IA) have equal kinetic energy of rotation. If LA and LB be their angular momenta respectively, then