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This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
A simple pendulum bob is given a horizontal velocity sqrt((7)/(2)gl) at the bottom. The string slackens after swinging through an angle theta with the vertical. The theta is |
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Answer» `30^(@)` |
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| 2. |
Consider a soap film on a rectangular frame of wire of area 4 xx 4 cm^(2). If the area of the soap film is increased to 4 xx 5 cm^(2), the work done in the process will be (The surface tension of the soap film is 3 xx 10^(-2)N//m) |
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Answer» `12 xx 10^(-6)J` `:.` Initial surface area of the film `=2 xx 4 xx 4 CM^(2) = 32 cm^(2) = 32 xx 10^(-4) m^(2)` Final surface area of the film `=2 xx 4 xx 5 cm^(2) = 40CM^(2) = 40 xx 10^(-4) m^(2)` Increase in surface area `= (40 xx 10^(-4) -32 xx 10^(-4)) m^(2) = 8 xx 10^(-4) m^(2)` Work done W= surface tension `xx` increase in surface area `=(3 xx 10^(-2) N//m) xx (8 xx 10^(-4) m^(2)) = 24 xx 10^(-6)J` |
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| 3. |
STATEMENT-1 The power of a thin lens does not depend upon the surrounding medium STATEMENT 2 power of a thin lens |
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Answer» STATEMENT -`1`is TRUE statement `2` is true,Statement -`2`is a correct explanation for statement -`1` |
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| 4. |
A satellite orbits the earth at a height of 400 km above the surface. How much energy must be expended to rocket the satellite out of the gravitational influence of earth ? Mass of the satellite is 200 kg, mass of the earth = 6.0 xx 10^(24) kg radius of the earth = 6.4 xx 10^(6)m, G = 6.67 xx 10^(-11) Nm^(2) kg^(-2). |
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Answer» Solution :TOTAL energy of ORBITING SATELLITE at a HEIGHT `h = (-GMM)/(2(R+h))` Energy expended to rocket the satellite out of the earth.s gravitational field = -(total energy of the satellite) `= (GMm)/(2(R+h)) = ((6.67 xx 10^(-11)) xx (6 xx 10^(24)) xx 200)/(2(6.4 xx10^(6) + 4 xx 10^(5))) = 5.9 xx 10^(9) J` |
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| 5. |
The accentricity of earth.s orbit is 0.067. Find the ratio of its maximum speed in its orbit to its minimum speed. |
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Answer» Solution :GIVEN ecentiality (e)=0.0167 `V_"MAX"/V_"MIN"=(1+e)/(1-e) =(1+0.0167)/(1-0.0167)`=1.033 |
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| 6. |
When the length of a simple pendulum is increased by 21% what is the change in its time period? |
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Answer» SOLUTION :Expression for the time period of a simple pendulum`T= 2pisqrt((l)/(g))` When length changes from `l_(1)` to `l_(2)` time period changes from `T_(1)` to `T_(2)` keeping g constant. `(T_(2))/(T_(1))= sqrt((l_(2))/(l_(1))):. (T_(2))/(T_(1))= sqrt((121l)/(100l))= (11)/(10)= ((T_(2))/(T_(1))-1)= ((11)/(10)-1)= (1)/(10) implies (DeltaT)/(T)%= (1)/(10)XX100= 10%` `:.` Increase in time period = 10% |
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| 7. |
Figure shows two rods each of length l placed side by side, with their facing ends separateed by a distance a.Chrges +q, -q reside on the rods as shown. Calculate the electric force on the rod A due to the rod B. Discuss the cases when lgtgta, agtgt1 |
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Answer» Solution :The FORCE on the rod A due to the charge +q of the rod B =- q^2/(4PI eplsilon_0(l+a0^2)+q^2/(4 pi eplsilon_0 a^2)` TOWARDS right. The force on this rod due to the charge -q. `q^2/(4 pi eplsilon_0(2l+a)^2) - q^2/(4 pi epsilon_0(l+a)^2)` towards right. The resultan force on the rod is `F= q^2 /(4 pi epsilon_0) [1/a^2-2/((l+a)^2)+1/((2l+a)^2)`]` towards right. If `lgtgta`, the last two terms in the square bracket are negligible as COMPARED to the first term. then, `F~~q^2/(4pi epsilon_0 a^2)` If `agtgt1` `F=q^2/(4 pi eplsilon_0) [1/a^2-2/a^2+1/a^2]~~0` Two neutral OBJECT placed far away exert only negligible force on each other but when they are placed closer they may exert appreciable force. |
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| 8. |
(A) : Mass and energy are not conserved separately, but are conserved as a single entity called mass - energy.(R ) : Mass and energy conservation can be obtained by Einstein equation for energy. |
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Answer» Both (A) and (R ) are TRUE and (R ) is the correct EXPLANATION of (A) |
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| 9. |
A pipe is running full of water. At a certain point A It tapers from 60 cm diameter to 20 cm at B. The pressure difference between A and B is 1 m of water column. Find the rate of flow of water through the pipe. |
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Answer» Solution :Let ` P_1 andP_2` be the pressure at A and B respectively and `v_1 and v_2`be the corresponding velocities Rate of flow = Velocity `xx` area of cross - section ` "" v_1 a_1= v_2a_2` ` v_1 pi r_1^(2)= v_2pi r_2^(2)` ` v_1 xx pi (0.3) ^(2)= v_2xx pi xx (0.1)^(2)` ` "" v_2 = 9 v_1` The gravitational potential energy remains constant By Bernouli.s theorem, ` P_1+(1)/(2)rho v_1^(2)= P_2+(1)/(2)rho v_2^(2)` `P_1- P_2 = (1)/(2)rho ( v_2^(2) - v_1^(2))` ` "" = (1)/(2)xx 1000 (8l v_1^(2)- v_1^(2))` But ` "" P_1 - P_2 =1 m " of water " ` ` ""9800 = 500 xx 80 v_1^(2)` `""v_1 ^(2) = ( 9800)/(500 xx 80 ) ` ` "" v_1 = 0. 495ms ^(-1) ` Rate of flow `"" a_1 v_1 = pi ( 0.3) ^(2) xx 0. 495` ` ""= 0. 1399 m ^(3)` per s |
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| 10. |
Two persons of equal weight are hanging by their hands from the ends of a rope hung over a frictionless pulley. They begin to climb the rope. One person can climb twice the speed of the other (with respect to the tope) Who will get to the top first? |
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Answer» The faster CLIMBER |
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| 11. |
Two bodies of unequal mass are moving in the same directionwith equal kinetic energy .The two bodies are brought to rest by applying regarding force of same magnitude . How would the distance moved by them before coming to rest compare ? |
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Answer» Solution :ACCORDING to work -energy THEOREM , `DeltaK = W` ` :. DeltaK = FD` As KE of the bodies and retarding forces applied on them are same , THEREFORE , both bodies will travel equal distances before coming to rest . |
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| 12. |
Spreading smoke of incense stick is an example of |
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Answer» ONE DIMENSIONAL motion |
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| 13. |
A piston can move freely inside a horizontal cylinder closed at both ends. Initially the piston divides the space inside of the cylinder into two equal parts each of volume V_0 and containing an ideal gas under the same pressure P_0 and at the same temperature T _0. What work must be done by the external agent in order to increase isothermally the volume of one part of the gas n times compared to that of the other by slowly moving the piston ? |
| Answer» SOLUTION :`P_0 V_0In ((n+1)^2)/(4N)` | |
| 14. |
A gun fires a bullet at a speed of 140 ms^(-1). If the bullet is to hit a target at the same level as the gun and at 1km distance, the angle of projection may be |
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Answer» `60^(@)` or `30^(@)` |
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| 15. |
A telescope has an objective lens of focal length 150cm and an eyepiece of focal length 5cm. IF a 50m tall tower at a distance of 1km is observed through this telescope in normal setting, the angle formed by the image of the tower is theta then theta is close to: |
| Answer» ANSWER :C | |
| 16. |
What are the degree of freedom in the following cases. |
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Answer» Solution :(i)A particel MOVES ALONG a straight line (i)One ,translational. (ii)A particle is projected in space (ii)Two,translational (iii)Motion of fan (ii)One,rotational (iv)Motion of ant. (iv)Two ,translational. (v)Motion of mosquito or FLY (no ROTAION) (v)Three,translational |
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| 17. |
Choose the pair physical quantities which have identical dimensions |
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Answer» IMPULSE & Linear momentum |
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| 18. |
Out of the following the correct order of dimensions of mass increases is A) Velocity B) Power C) Gravitational constant |
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Answer» A, B, C |
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| 19. |
The time period of a body suspended from a spring is T. The new time period if it is cutting to three equal parts and same mass suspended for one part, the new time period is |
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Answer» `SQRT(2)T` |
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| 20. |
In Bernoulli's theorem which one of the following is conserved? |
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Answer» mass |
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| 21. |
If a sphere rolls (starting from rest) in 5.3 s along a plane1m in length of which the upper end is raised above the lower. Find the acceleration due to gravity. |
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Answer» |
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| 22. |
A ball at rest is dropped freely from a height of 20 m. It loses 30% of its energy on striking the ground and bounces back. Theheight to which it bounces back us |
| Answer» ANSWER :A | |
| 23. |
A glass U-tube is inverted with open ends of the straight limbs, of diameters 0.5 mm and 1.0 mm below the surface of water in a beaker. The air pressure in the upper part is increased until the meniscus in one limb is level with the water outside. Find the height (cm) of water in the other limb in nearest integer. : (Density of water is 10^(3)Kg//m^(3) and surface tension of water is 7.5 xx 10^(-2)N//m. Take contact angle theta = 0^(@)) |
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Answer» |
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| 24. |
A ball is thrown vertically upwards. Which of the following plots represents the speed-time to the ball during its flight if the air resistance is not ignored? |
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Answer»
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| 25. |
What force is required to stretch a copper wire Icnr in crossection to double its length7 (Y=1.3xx10^(11)N//m^(2)). |
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Answer» SOLUTION : Stress =F/A. Strain = `(2l-l)/(I)=1` `:.=("Stress")/("strain")="STRES" =1.3xx10^(11)N//m^(2) :. F="stress" xx A=1.3xx10^(11)xx(1)/(10^(4))=1.3xx10^(7)N` |
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| 26. |
A thin disc of radius R and mass M is free to rotate about a vertical axis passing through its centre and perpendicular to its plane. The disc in initially at rest. A small of mass M/3 is walking along the rim of the disc with a relative speed 'v' with respect to the surface of the disc. What is the angular velocity with which the disc rotates in the opposite direction ? |
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Answer» `(V)/(5R)` |
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| 27. |
A simple pendulum hanging freely and at rest is vertical because in that position |
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Answer» K,E is ZERO |
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| 28. |
One side of a cube is measured as a = 4.03 pm 1%. What is its volume? |
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Answer» Solution :Volume `=a^(2)= (4.03m +- 1%)^(3)` `= 4.03^(3) m^(3) +- (3 XX 1)%` `=65.45 m^(3) +- 3%` |
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| 29. |
All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up. |
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Answer»
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| 30. |
Which of the following two parameter have same dimension? (a) energy density(b) refractive index (c) dielectric constant (d) Young's modulus (e) electric field. |
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Answer» (b) and (d) `=(ML^(2)T^(-2))/(L^(3)) =ML^(-1)T^(-2)` [REFRACTIVE index] `([c])/([v])` `=(LT^(-1))/(LT^(-1))=M^(0)L^(0)T^(0)` where c= speed of ligth in VACCUM v= speed of LIGHT in medium [dielectric constant] `=([E])/([E_(0)])=M^(0)L^(0)T^(0)` where E and `E_(0)` are permittivity in medium and vaccum. [Young.s MODULUS] `=("Stress")/("Strain")` `=([F][l])/([A][Deltal])` `=((MLT^(-2))(L))/((L^(2))(L))` `=ML^(-1)T^(-2)` [Magnetic FIELD `(B)=(F)/(I l sin theta)[ L, F= BI l sin theta]` `sin theta` is dimensionless. `[B]=([F])/([I][l][sin theta])` `=(MLT^(-2))/((A)(L)(M^(0)L^(0)T^(0))` `:.` Option (C) is correct |
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| 31. |
What is temperature gradient ? |
| Answer» SOLUTION :The difference in temperature DISTANCE between TWO parts of solid is called temperature GRADIENT. | |
| 32. |
A student records triangleQ, triangleU & triangleW for a thermodynamic cycle A rarrBrarrCrarrA. Certain entries are mikssing. Find correct entry in following options. |
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Answer» `W_BC = -70J` |
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| 33. |
Phase difference between two waves y _(1) = A sin (omega t - kx) and y _(2)= A cos (omega t - kx)is …… |
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Answer» `pi/4` ` y _(2) = A cos (omega t - kx )` `therefore y _(2) = A sin ((pi)/(2) + omega t - kx)` `(because cos THETA = sin ((pi )/(2) + theta ))` Phase difference `= ((pi)/(2) + omega t - kx) - (omega t - kx)` br> `= (pi)/(2) + omega t - kx - omega t + kx` `=(pi)/(2) RAD` |
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| 34. |
The fundamental unit which has the same power in the dimensional formula of surface tension and viscosity is |
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Answer» mass |
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| 35. |
A car starts from rest and moves on a surface with uniform acceleration. Draw the graph of kinetic energy versus displacement. What information you can get from that graph ? |
Answer» SOLUTION : A car starts from and move with uniform acceleration. The graph between kinetic ENERGY and displacement straight line The SLOPS of KE and displacement graph give net force ACTING onthe car to keep the car withuniform acceleration |
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| 36. |
A rod of length 1 and radius .r. is joinedto a rodof lengthl//2 and radiusr//2 of same material. The free of small rod is fixed to a rigid base and the free end of larger rod is given a twist of theta. The twist angle at the point will be |
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Answer» Solution :`theta_(1)+theta_(2)=theta to (1)` we know that `theta PROP (l)/(r^(4))` `therefore (theta _(1))/(theta_(2)) =(l_(1))/(l_(2)) XX (r_(2)^(4))/(r_(1)^(4)) =(l//2)/(l)xx (r^(4))/((r//2)^(4)) =8`  `(theta_(1))/(theta_(2))=8"" to (2)` After solving equations (1) and (2), we GET `theta_(1)=(8)/(9) theta` |
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| 37. |
A copper sphere is suspended in an evacuated chamber maintained at 300 K. The sphere is maintained at a constant temperature of 500 K by heating it electrically. A total of 210 W of electric power is neede to do it. When the surface of the copper sphere is completely blackened, 700 W is needed to maintain the same temperature of the sphere. The emissivity of copper is _______ xx10^(-1) |
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Answer» |
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| 38. |
The point at which whole mass of object is centred it is called …... . |
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Answer» |
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| 39. |
A bird moves in such a way that it has a displacement of 12 m towards east, 5 m towards north and 9m vertically upwards. Find the magnitude of its displacement. |
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Answer» `5sqrt(2)m` |
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| 40. |
A converging lens of focal length 5.0cm is placed in contact with a diverging lens of focal length 10.0cm. Find the combined focal length of the system. |
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Answer» SOLUTION :Here `f_1=+5.0cm and f_2=-10.0cm` THEREFORE, the combined FOCAL length F is GIVEN by `1/F=1/f_1+1/f_2=1/5.0-1/10.0=+ 1/10.0` `therefore F=+10.0cm` i.e, the combination behaves as a converging lens of focal length 10.0cm |
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| 41. |
A vertical rod free to rotate about 'O' as shown. It begins to rotate. When it has turned through an angle 'theta'. Its angular velocity 'w' is given as |
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Answer» `sqrt((6g)/(L))SINTHETA` |
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| 42. |
A particlemoves form x = 0 to x = 2 m onX - axisunder the effect of a forcevec(F)x = (4x^(3) -3x^(2)+2x) hat(i) newton . The workdone on the particle is |
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Answer» 22 Joule ` :."Work done " W = int_(0)^(2) vec(F) . D vec(x)` ` = int_(0)^(2) (4x^(3) -3x^(2) +2x+5) hat(i) . hat(i) dx ` `= 4[(x^(4))/4]_(0)^(2) -3[(x^(3))/3]_(0)^(2) +2[(x^(2))/2]_(0)^(2)` ` + 5[x]_(0)^(2)` ` ( :. intx^(n)dx = (x^(n+1))/(n+1))` ` = 16 - 8 + 4 + 10 ` ` :. W = 22 J ` |
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| 43. |
A sphere can roll on a surface inclined at an angle theta if friction coefficient is more than (1)/(7)"g "tantheta If a sphere is released from rest on the incline |
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Answer» it will stay at REST |
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| 44. |
A fluid is in streamline flow across a horizontal pipe of variable area of cross section. For this which of the following statements is correct? |
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Answer» The velocity is MAXIMUM at the NARROWEST PART of the pipe and pressure is maximum at the widest part of the pipe |
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| 45. |
The time period of an earth satellite in circular orbit is independent of |
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Answer» The MASS of the SATELLITE |
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| 46. |
An elevator ascends with an upward acceleration of 0.2m//s^(2). At the instants its upward speed is 3m//sec a loose bot 5m high from the floor drops from the ceiling of the elevator. Find the time until the bolt strikes the floor and the displacement it has fallen |
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Answer» Solution :Initial VELOCITY of bolt relative to the floor of ELEVATOR = 0 acceleration of bolt relative to the floor of the elevator = `(9.8+0.2)=10ms^(2)` If t is time of the DESCENT then `5=(1)/(2)xx10xxt^(2)` `therefore t=1` SECOND If s is the displacement then `s=-ut+(1)/(2)g t^(2)` `s=-3(1)+(1)/(2)(9.8)(1)^(2) therefore s=1.9m` |
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| 47. |
At every point of rest liquid, the tangential stress is zero. Explain with reason. |
| Answer» Solution :If at any point of LIQUID having TANGENTIAL stress then liquid MOVES or flow to beside but this does not HAPPEN. That means at every point of liquid the tangential stress is ZERO. | |
| 48. |
The spin drier of a washing machine revolving at 15 r.p.s slows down to 5 r.p.s., while making 50 revolutions. Find (a) angular acceleration and(b) time taken. |
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Answer» Solution :Here `omega_(0)=15 r.p.s = 30 pi rad s^(-1)` `ometa_(0)=5 r.p.s. = 10 pi rad s^(-1)` `theta = 50xx2pi=100 pi` Rad (a) Now, `omega^(2)-omega_(0)^(2)=2alpha theta` `THEREFORE (10 pi)^(2)-(30PI)^(2)=2alpha xx100 pi` or `alpha = -4 pi rad s^(-2)` (b) Also, `omega= omega_(0)+alpha t` `therefore 10 pi = 30 pi +(-4PI)XX t` or t = 5 s. |
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| 49. |
The separation between two microscope particles is measured P_A and P_B by two different lights of wavelengths 2000A and 3000A respectively, then |
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Answer» `P_A GT P_B` |
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