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This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 14501. |
Two masses of 10 kg and 5 kg are suspended from a rigid support as shown in figure. The system is pulled down with a force of 150 N attached to the lower mass. The string attached to the support breaks and the system accelerates downwards. In case the force continues to act. what will be the tension acting between the two masses ? |
| Answer» Solution :`F=ma, a=(F)/(m), T=m(a-g)` | |
| 14503. |
A block of mass mass suspended by a rubber cord of natural lengthl = (mg)/Kwhere K is force constant of the cord. The block is lifted upward so that the cord becomes just tight and then block is released suddenly: |
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Answer» Block performs PERIODIC motion with amplitude greater than L. |
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| 14504. |
A small bottle of an ideal gas is brought into a thermally insulated room and it is broken in the room. What happens to the temperature of the room? |
| Answer» SOLUTION :It remains constant, as free EXPANSION of the gas does no work, DW= 0 and no HEAT is supplied dQ=0::dŲ =0 or U=constant. | |
| 14505. |
Assertion:The shape of an automobile is so designed that its front resembles the streamline pattern of the fluid through which it moves.Reason:The resistance offered by the fluid is maximum.Select the correct option from the following options. |
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Answer» Both ASSERTION and REASON are TRUE and reason explains assertions correctly. |
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| 14506. |
A wind power generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by blades into electrical energy. If wind speed is v, power delivered is proportional to v. Then the value of x. |
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| 14507. |
Statements : (a) The motion of the centre of mass can be studied using kepler.s laws of motion. (b) The internal forces will not effect the motion of the centre of mass |
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Answer» Both a and B are TRUE |
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| 14508. |
The potential energy of a 1 kg particle free to move along the x-axis is given by V(x) ((x^4)/4 - (x^2)/2)J The total mechanical energy of the particle is 2 J. Then, the maximum speed (in m/s) is |
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Answer» 2 For maximum SPEED. KINETIC energy is maximum. The potential energy should therefore be minimum. As `V (x) = (x^4)/(4) - (x^2)/(2)` `:. (DV)/(dx) = (4x^3)/(4) - (2x)/(2) = x^3 - x = x(x^2 -1)` For V to be minimum, `(dV)/(dx) = 0` `:. x(x^2 - 1) = 0 , "or " x = 0, pm 1` At `x = 0, V(x)= 0` and at `x = pm 1, V(x) = -1/4 J` `:. ("Kinetic energy")_("max") = E_T - V_("min")` or `("Kinetic energy")_("max")= 2 - (-1/4) = 9/4 J`. or `1/2 mv_("max")^(2) = 9/4"or " v_("max")^(2) = (9 xx 2)/(m xx 4) = (9 xx 2)/(1 xx 4) = 9/2` `:. v_("max") = 3/(sqrt2) m//s` . |
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| 14509. |
One end of a cylindrical glass is given the shape of the concave refracting surface of radius 10cm. An air bubble is situated in the glass rod of a point on its axis such that it appears to be at distance 10cm from the surface and inside glass when seen from the other medium. Find the actual location of air bubble |
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Answer» SOLUTION :`mu_2/v-mu_1/v=(mu_2-mu_1)/R` Here `mu_1=1.5, mu_2=1` `v=-10cm, R=+10 cm` `THEREFORE -1/10-1.5/u=(1-1.5)/10=-1/20` `=1.5/u=1/10+1/20=-1/20 therefore u=-30 cm` HENCE the air bubble is actually located at a distance 30 cm from the surface and inside glass. 
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| 14510. |
The block is placed on a frictionless surface in gravity free space. A heavy string of a mass m is connected and force F is applied on the string, then the tension at the middle of rope is |
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Answer» `(((m)/(2)+M).F)/(m+M)` |
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| 14511. |
A rectangle has a length = 4.234 m and breadth = 1.05 m. What is its area in m^(2) ? Keep the significant digits only. |
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Answer» 4.4457 |
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| 14512. |
The intensity of radiation emitted by the Sun has its maximum value at a wavelength of 510 nm and that emitted by the North Star has the maximum value at 350 nm. If these stars behave like black bodies, then the ratio of the surface temperatures of the Sun and the North Star is : |
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Answer» 1.46 |
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| 14513. |
The total mechanical energy of a harmonic oscillator of amplitude Im and force constant 200 N/m is 150J. Then |
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Answer» The MINIMUM PE is zero |
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| 14514. |
Which of the following is not a perfectly inelastic collision? |
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Answer» STRIKING of two GLASS bulbs |
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| 14515. |
A person holds a block weighing 2kg between his hands & keeps it from down by pressing it with his hands. If the force exerted by each hand horizontally is 50 N, the co-efficient of friction between the hand & the block is (g=10 ms^(-2)) |
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Answer» `0.2` |
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| 14516. |
A vector A makes on angle 30° with the y-axis in anticlockwise direction. Another vector B makes on angle 30° with the x-axis in clockwise direction. Find angle between yectors A and B. |
Answer» SOLUTION : From the diagram the angle between `vec(A)` and `vec(B)` is `30^(@) + 90^(@) + 30^(@) = 150^(@)` |
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| 14517. |
Two ships are 10 km apart on a line from south to North. The one further North is moving towards West at 40 km/hr and other is moving towards North at 40 km/hr. The distance of closest approach is |
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Answer» 5 KM |
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| 14518. |
Consider the following statements .A. and .B. and identify the correct answer.A : In an elastic collision, if a body suffers a head on collision with another of same mass at rest, the first body comes to rest while other starts moving with the velocity of first one.B : Two bodies of equal masses suffering a head on elastic collision exchange their velocities. |
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Answer» Both A and B are TRUE |
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| 14519. |
A spring of unstretched length l has a mass m one end fixed to a rigid support. Assumingspring to be made of a uniform wire, the kinetic energy possessed by it if its free end is pulled with uniform velocity upsilon is: |
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Answer» `(1)/(2)mupsilon` |
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| 14520. |
A small spherical ball of radius r falls freely under gravity through a distance h before entering a tank of water. If, after entering the water, the velocity a of the ball does not change. Then h is proportional to |
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Answer» `r^2` |
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| 14521. |
A block of mass M is kept on a frictionless horizontal table. A body of mass m is kept on the block. If a force F, Parallel to the table top is applied on the block, the body on the block tends to slide backwards. What is the coefficient of static friction between the block and the body? |
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| 14522. |
The minimum and maximum distance of a satellite from the centre of the earth 2R and 4R respectively. Where R is the radius of the earth and M is the mass of earth. Its maximum speed is: |
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Answer» `SQRT((GM)/(6R))` |
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| 14523. |
A planet revolves around sun in an elliptical orbit of eccentricity .e. . If .T. is the time period of the planet then show that the time spent by the planet between the end of the minor axis and close to sun is T (1/4-(e)/(2pi)) |
Answer» SOLUTION :`(dA)/(DT) ` = CONSTANT t ,  `(t_(AB))/(T) = (("AREA")"SAB")/("(Area) ellipse")=((piab)/(4)-1/2b(""ea))/(piab)` |
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| 14524. |
In the above problem, the initial speed with which water strikes the ground in ms^(-1) is |
| Answer» Solution :`v_(x)=sqrt(2gh_(1)), v_(y)=sqrt(2gh_(2)), v=sqrt(v_(x)^(2)+v_(y)^(2))` | |
| 14525. |
Two car s A and B are moving west to east and south to north respectively along crossroads. A moves with a speed of 72kmh^(-1) and is 500 m away from point of intersection of cross roads and B moves with a speed of 54kmh^(-1) and is 400 m away from point of intersection of cross roads. FInd the shortest distance between them? |
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| 14526. |
(A) : A physical quantity cannot be called as a vector if its magnitude is zero. ( R) : A vector has both magnitude, direction without satisfying vector addition properties. |
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Answer» Both (A) and ( R) are ture and ( R) is the CORRECT explanation of (A) |
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| 14527. |
When does a cyclist appear to be stationaly with respect to another moving cyclist ? |
| Answer» SOLUTION :When both the CYCLISTS are MOVING in the same direction with the same velocity PARALLEL to each other . | |
| 14529. |
When a satellite isorbitting round a planet in circular orbit, workdone by the gravitational force acting on the satellite is |
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Answer» ZERO on completing ONE revolution only |
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| 14530. |
Earth completes one revolution round the sun in 365.25 days. What is the angular velocity ? |
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Answer» Solution :Angle subtended for ONE revolution `=THETA = 360^(@) = 2pi` rad TIME taken `=T = 365.25` days = `365.25 xx 24 xx 60 xx 60` ANGULAR velocity `=omega = (2pi)/T = (2 xx 3.14)/(365.25 xx 24 xx 60 xx 60)` `= 1.9 xx 10^(-7)` rad/s |
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| 14531. |
State in the following cases, whether the motion is one, two or three dimensional: A carrom coin rebounding smoothly from the side of the board. |
| Answer» SOLUTION :TWO DIMENSIONAL | |
| 14532. |
A particle falls from a height h on a fixed horizontal plate and rebounds. If e is the coefficient of restitution, the total distance travelled by the particle before it stops rebounding is |
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Answer» `(H(1 + e^2))/((1 - e^2))` `S = h + 2e^2 h + 2e^4 h + 2e^6h + ……` `= h + 2H (e^2 + e^4 + e^6 + ….)` `= h + 2h ((e^2)/(1 - e^2)) = h[1 + (2e^2)/(1 - e^2)] = (h(1 + e^2))/((1 - e^2))` |
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| 14533. |
In the following 'I' refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity |
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Answer» `M^(-1)L^(-3)T^(-3)I` |
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| 14534. |
A spring of spring constant 5 xx 10^3. N m^(-1) is stretched initially by 5 cm from the unstretched position. The work required to stretch it further by another 5 cm is |
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Answer» 6.25 Nm `U_2 = 1/2 kx_2^2 = 1/2 xx 5 xx 10^(3) xx (5 + 5)^2 xx 10^(-4)= 25 Nm`. `:. ` WORK done = `U_2 - U_1 = 25.0 Nm - 6.25 N m = 18.75 Nm`. |
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| 14535. |
Separation of motion of a system of particles into motion of the centre of mass and motion about the centre of mass: (a)n Show vecp= vecp_(i)+m_(i)vecV where vecp_(i) is the momentum of the i^(th) particle (of mass m_(i)) and vecp_(i)=m_(i)vec v_(i), Not vec v_(i) is the velocity of the i^(th) particle relative to the centre ofmass. Also, prove usingthe definition of the centre of mass sum vec p_(i)=0 (b) Show K=K'+""_(1//2)MV^(2) where K is the total kinetic energy of the system of particles, K is the total kinetic energy of the system when the particle velocities are taken with respect to the centre of mass and MV^(2)//2 is the kinetic energy of the translation of the system as a whole (i.e. of the centre of mass motion of the system) (c) Show vecL= vecL+ vecR xxMV where vecL'=sum vec r_(i) xx vec p_(i) is the angular momentum of the system about the centre of mass with velocities taken relative to the centre of mass. Remember vecr_(i)=vecr_(i)-vecR, reat of the notation is the standard notation used in the chapter. Note vecL' and M vecR xx vecV can be said to be angular momenta, respectively, about and of the centre of mass of the system of particles. (d) Show (d vecL)/(dt)= sum vecr_(i)xx(d vecp')/(dt) Further show that (dvecL')/(dt)= vec tau_(ext)'where Text is the sum of all external torques acting on the system about the centre of mass. (Hint: Use the definition of centre of mass and Newton's Third Law. Assume the internal forces between any two particles aet along the line joining the particles.) |
| Answer» SOLUTION :REFER to THEORY. | |
| 14536. |
A wooden block is placed on an inclined plane. The block just begins to slide down when the angle of the inclination is increased to 45^(@). The coefficient of the friction is |
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Answer» `0.25` |
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| 14537. |
You are riding in an automobile of mass 3000 kg. Assuming that you are examining the oscillation characteristics of its suspension system. The suspension sags 0.15 m when the entire automobile is placed on it. Also, the amplitude of oscillation decreases by 50% during one complete oscillation. Estimate the value of (a) the spring constant k and (b) damping constant'b' for the spring and shock absorber system of one wheel, assuming that each wheel supports 750 kg (g=10ms^(-2)). |
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Answer» SOLUTION :Given, `M=3000kg""m=750kg` Since the WEIGHT is supported on 4 shocks `Mg=-4ky` hence spring constant `k=(3000xx10)/(4xx0.15)` `"i.e."k=5xx10^(4)Nm^(-1)` (b) Mass supported by each spring `=(3000)/(4)=750kg` using`""y=Ae^(-bt//2M) and t=T""y=(A)/(2)and log_(e)=2=0.693` `"or"(bt)/(2m)=0.693"or"b=(2xx750xx0.693)/(T)` `"i.e."b=(1039.5)/(T)` `"where"T=2pisqrt((M)/(4k))=2xx3.142xxsqrt((3000)/(4xx5xx10^(4)))` `"i.e."T=0.7698s` `"hence"b=(1039.5)/(0.768)` `b=1.350xx10^(3)" kgs"^(-1).` |
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| 14538. |
When an elastic material (Y = E) is subjected to a stress S, find the elastic energy per unit volume. |
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| 14539. |
The temperature of an isolated black body falls from T_(1) to T_(2) in time t. Let c be a constant |
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Answer» `t = c [(1)/(T_(2)) - (1)/(T_(1))]` `int_(T_(1))^(T_(2)) (dT)/(T^(4)) = - sigma A int_(0)^(t) dt` `[(1)/(T_(2)^(3)) - (1)/(T_(1)^(3))] = (3 sigma A) t` `t - (1)/((3 sigma A)) [(1)/(T_(2)^(3)) - (1)/(R_(1)^(3))]` `t = c [(1)/(T_(2)^(3)) - (1)/(T_(1)^(3))], c = (1)/(3 sigma A)` |
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| 14540. |
A simple pendulun executes SHM approximately.Why then is the time period of a simple pendulum independent of the mass of the pendulum? |
| Answer» SOLUTION :T=`2pisqrt(l/g)`. This EQUATION shows that PERIOD is independent of mass of pendulum. | |
| 14541. |
A stone thrown vertically up with velocity reaches three points A, B and C with velocities v/2, v/4 and v/8respectively. Then AB:BC is |
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Answer» `1:1` |
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| 14542. |
A railway engine of mass 50 ton is pulling a wagon of mass 40 tons with a force of 4500N. The resistance force acting is IN per ton. The tension in the coupling between the engine and the wagon is |
| Answer» Answer :B | |
| 14543. |
From the top of a tower 100 m in height a ball is dropped and at the same time another ball is projected vertically upwards from the ground with a velocity of 25 m/s. Find when and where the two balls will meet? (g=9.8m/s) |
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Answer» Solution :For the BALL dropped from the TOP `x=4.9t^(2)""......(1)` For the ball thrown upwards `100-x=25t-4.9t^(2)""......(2)` From EQ. (1) and (2) `t=4s,x=78.4m` |
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| 14544. |
Four small spheres each of radius .r. and mass .m. are placed with their centres at the four corners of a square of side .L.. The M.I. of the system about any side of square is |
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Answer» `(8mr^(2))/(5)+ML^(2)` |
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| 14545. |
When the axis of rotation of a body changes does moment of inertia also change ? Why ? |
| Answer» SOLUTION :Yes, because the mass DISTRIBUTION changes, i.e., the distances of the particles from the AXIS CHANGE. | |
| 14546. |
At its aphelion the planet mercury is 7 xx 10^(10) m from the sun & at its perihelion it is 4.5 xx 10^(10) m from the sun. IF the speed of mercury at aphelion is 3.6 xx 10^(4) m/s. then speed of it at perihelion is |
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Answer» `3.6 XX 10^(4)` m/s |
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| 14547. |
The gravitational potential energy of interaction of a system of six identical particles, each of mass m placed at the vertices of a regular hexagon of side .a. is [PE = 0 at infinite separation] |
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Answer» `-(Gm^(2))/(a) (1 + (1)/(SQRT(3)) + (1)/(4))` |
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| 14548. |
barA and barB are two vectors which act at a point simultaneously so that they form the adjacent sides of a parallelogram. If barC and barD are diagonals of the parallelogram, find the area of parallelogram. |
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| 14549. |
In Fig.a man stands on a boat floating in still water. The mass of the man and the boat is 60 kg and 120 kg,respectively. a. If the man walks to the front of the boat and stops. what is the separation between the boat and the pier now? b. If the man moves at a constant speed of 3 m//s relative to the boat, what is the total kinetic energy of the system (boat + man)? Compare this energy with the kinetic energy of the system if the boat was tied to the pier. |
Answer» Solution : a. DISPLACEMENT of MAN w.r.t boat `x_(m,b)=6m` `x_(b)=x_(m,b)(m_(1)/(m_(1)+m_(2)))=-6xx30/(60+20)=-2m` Therefore, boat displaces by `2 m` away from the PIER. `:.` Seperation `=2.5m` b. `vecv_(mb)=vecvm-vecvb` `m_(1)vecv_(m)+m_(2)vecv_(b)=0` `m_(1)(vecv_(mb)+vevcb)+m_(2)vecv_(b)=0` `m_(1)v_(mb)=(m_(1)+m_(2))v_(b)` `v_(b)=(m_(1)/(m_(1)+m_(2)))v_(mb)` `v_(b)=60/180xx3=1m//s` `KE` of the man `=1/2m_(m)v_(m)^(2)=1/2xx60xx(3-1)^(2)=120J` `KE` of the boat `=1/2xx120xx(1)^(2)=60J` TOTAL `KE` energy `=120+60=180J` `KE` of the sytem when the boat is tied `=1/2x60xx3^(2)=270J` |
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| 14550. |
Can wemeasurethetemperatureof theobjectby touching it ? |
| Answer» SOLUTION :No, we can.t measure the temperature of the object TOUCHING it. Because the temperature is the DEGREE of HOTNESS or coolness of a body. Only we can sense the hotness or coolness of the object. | |