72 + Interview Questions in RIGID-BODIES-AND-ROTATIONAL-MOTION IN GENERAL AWARENESS Page 2 InterviewSolution

51.	A thin circular ring of mass M and radius r is rotating about its ais with an angular speed `omega`. Two particles having mas m each are now attached at diametrically opposite points. The angular speed of the ring will becomeA. `(omega M)/(M+ m)`B. `(omega M)/(M+ 2m)`C. `(omega(M-2m))/(M+2m)`D. `(omega(M+2m))/(M)`
Answer» Correct Answer - D

Discussion

52.	A grindstone in the form of a solid cylinder has a radius of 0.2m and a mass of 30 kg. (a)What constant torque will bring it from rest to an angular velocity of 250 rev`//`min in 10 s ? (b) Through what angle has it turned during that time ? (c) Calculate the work done by the torque.
Answer» Correct Answer - [`1.57 kg cdotm^(2),2.29 N-m, 58.3 rev`]

Discussion

53.	A rectangular rigid fixed block has a long horizontal edge. A solid homogeneous cylinder of radus R is placed horizontally at rest its length parallel to the edge such that the exis of the cylinder and the endg of the block are in the same vertical plane as shown in the figure below. Ther is sufficinet friction present at the edge s that a very small displacement causes the cylinder to roll off the edge without slipping. Determine: (a) the angle `theta_c` through which the cylinder rotates before it leaves contact with the edge, (b) the speed of the centre of mass of the cylinder before leaving contact with the edge, and (c) the ratio of the translational to rotational kinetic energy of the cylinder when its centre of mass is in horizontal line with the edge.
Answer» Correct Answer - [`cos^(-1)"(3g)/(2omega^(2)l),1//2momega^(2)lsqrt1+(7g^(2))/(4omega^(4)l^(2)),cosphi=(4costheta)/(sqrt(9+7cos^(2)theta))`]

Discussion

54.	A particle is revolving in a circular path as shownin figure in the horizontal plane such that the angular velocity of the particle about the point O is constant and is equal to `1 rad//s`. Distance of the particle from O is given by`R=R_(0)-betat` where `R_(0)`and `Beta` are constant. The speed ofthe particle,as afunction of time is: ltbrlt A. `sqrt(beta^(2)+1)`B. `(R_(0)-beta t)`C. `sqrt(beta^(2)+(R_(0)-beta t)^(2))`D. `beta`
Answer» Correct Answer - C

Discussion

55.	A uniform ring of mass m and radius R is in uniform pure rolling motion on a horizontal surface. The velocity of the centre of ring is `V_(0)`. The kinetic energy of the segment ABC is: A. `(mV_(0)^(2))/(2)-(mV_(0)^(2))/(pi)`B. `(mv_(0)^(2))/(2)+(mv_(0)^(2))/(pi)`C. `(mv_(0)^(2))/(2)`D. `mv_(0)^(2)`
Answer» Correct Answer - A

Discussion

56.	A 392 N wheel comes off a moving truck and rolls without slipping along a highway. At the bottom of a hill it is rotating at 50 rad`//`s. The radius ofthewheel is 0.6m, and its moment of inertia about its rotation axis is `0.8MR^(2)`. Friction does 3000 J of work on the wheel as it rolls up the hill to a stop a height h above the bottom of the hill. Calculate h.
Answer» Correct Answer - [29.1 m]

Discussion

57.	The wheel of radius R rolls with out slipping on horizontal rough surface, and its centre O has an horizontal acceleration in `a_(0)` forward direction. A point P on the wheel is a distancer `r` from O and angular position `theta` from horizontal. For the given values of `a_(0)` R and r, determine the angle `theta` for which point P has no acceleration in this position. A. `cos^(1).(r)/(R)`B. `tan^(1).(r)/(R)`C. `sin^(1).(r)/(R)`D. `cos^(1).(r)/(2R)`
Answer» Correct Answer - C

Discussion

58.	A point A is located on the rim of a wheel of radius R which rolls witout slipping along a horizontal surface witih velocity V. Find the total distance traversed by the point A between successive moments at which it touches the surface.
Answer» Correct Answer - `[8r]`

Discussion

59.	A carpet of mass `M` is rolled along its length so as to from a cylinder of radius `R` and is kept on a rough floor. When a negligibly small push is given to the cylindrical carpet, it stars unrolling itself without sliding on the floor. Calculate horizontal velocity of cylindrical part of the carpet when its radius reduces to `R//2`.
Answer» Correct Answer - `[sqrt((14gR)/(3))]`

Discussion

60.	A particle moves with a constant velocity parallel to the X-axis. Its angular momentum with respect to the originA. Is constantB. Is constantC. Goeson increasingD. Goes on decreasing
Answer» Correct Answer - B

Discussion

61.	The centre of a wheel rolling on a plaen surface moves with a speed `v_0`. A particle on the rim of the wheel at the same level as the centre will be moving at speedA. ZeroB. `v_(0)`C. `sqrt(2)V_(0)`D. `2v_(0)`
Answer» Correct Answer - C

Discussion

62.	A uniform disc of mass m and radius R is projected horizontally with velocity `v_(0)` on a rough horizontal floor so that it starts with a purely sliding motion at t= 0. After `t_(0)` seconds it acquires a purely rolling motion. (a) Calculate the velocity of the centre of mass of the disc at `t_(0)` (b) Assuming the coefficient of friction to be `mu`, calculate to. Also calculate the work done by the frictional force as a function of time and the total work done by it over a time t muchlonger than `t_(0)`.
Answer» Correct Answer - `[v_(0)//3,(1)/(2)mmu"gt"(2v_(0)-3mu"gt")]`

Discussion

63.	A particle of mass m is projected with a velocity `mu` at an angle of `theta` with horizontal.The angular momentum of the particle about the highest point of its trajectory is equal to :A. `("mu"^(3)sin^(2)thetacostheta)/(3g)`B. `(3"mu"^(3)sin^(2)thetacostheta)/(3g)`C. `("mu"^(3)sin^(2)thetacostheta)/(2g)`D. `(2"mu"^(3)sinthetacos^(2)theta)/(3g)`
Answer» Correct Answer - C

Discussion

64.	A uniform sphere of mass m and radius r rolls without slipping down a inclined plane, inclined at an angle `45^(@)` to the horizontal . Find the magnitude of frictional coefficient at which slipping is absent :A. `(1)/(3)`B. `(2)/(7)`C. `(1)/(5)`D. `(1)/(7)`
Answer» Correct Answer - B

Discussion

65.	A particle is projected at time t=0 from a point P on the ground with a speed `v_0,` at an angle of `45^@` to the horizontal. Find the magnitude and direction of the angular momentum of the particle about P at tiem `t= v_0//g`
Answer» Correct Answer - `"["(mv_(0)^(3))/(2sqrt2g)"]"`

Discussion

66.	Two identical discs are moving with the same kinetic energy. One rolls and the other slides. The ratio of their speeds is:A. `1:1`B. `sqrt(2): sqrt(3)`C. `2:3`D. `1:2`
Answer» Correct Answer - B

Discussion

67.	A solid cylinder is relased from rest from the top of an inclined plane of inclination `60^@` where friction coefficient varies with distance `x` as `mi = (2 - 3x)/(sqrt(3))`. Find the distance travelled by the cylinder on incline before it starts slipping.A. 1/3 mB. `1//sqrt(3)` mC. 3 mD. `sqrt(3) m`
Answer» Correct Answer - A

Discussion

68.	The moment of inertia of the pulleys system as shown in the figure-5.103 is 4 `kgm^(2)` The radii of bigger and smaller pulleys 2 mand 1m respectively.The angular acceleration of the pulley system is: (take `= 10 m//s^(2)`) A. `2.1 rad//s^(2)`B. `4.2 rad//s^(2)`C. `1.2 rad//s^(2)`D. `0.6 rad//s^(2)`
Answer» Correct Answer - A

Discussion

69.	A ladder of length `5 m` is placed against a smooth wall as shown in figure. The coefficient or friction is `mu` between ladder and ground. What is the minimum value of `mu` , If the ladder is not to slip? A. `mu=(1)/(2)`B. `mu=(1)/(4)`C. `mu=(1)/(3)`D. `mu=(1)/(5)`
Answer» Correct Answer - C

Discussion

70.	A rod of mass m and length l is held vertically on a smooth horizontal floor. Now it is released from this position, find the speed of its centre of mass when it makes an angle `theta` with the vertical.
Answer» Correct Answer - [`(sqrt(6gl)sin"(theta)/(2)costheta)/(sqrt1+3sin^(2)theta)`]

Discussion

71.	A block of mass `m` is held fixed against a wall by a applying a horizontal force `F`. Which of the following option is incorrect : .A. frictional force f=mgB. normal reaction N=FC. F will not produce a torqueD. N will not produce any torque
Answer» Correct Answer - D

Discussion

72.	A uniform ring placed on a rough horizontal surface is given a sharp impulse as shown in the figure-5.130. As a consequence, it acquires a linear velocity of 2m/s. If coefficient of friction between the ring and the horizontal surface is 0.4 : A. Ring wil lstart pure rolling afler O.25sB. When ring will start pure rolling its .velocity is 1m//sC. After 0.5s from impulse its velocity is 1m//s.D. After0.125 s from impulse its velocity is 1m//s.
Answer» Correct Answer - A::B::C

Discussion

Explore topic-wise InterviewSolutions in .

A grindstone in the form of a solid cylinder has a radius of 0.2m and a mass of 30 kg. (a)What constant torque will bring it from rest to an angular velocity of 250 rev`//`min in 10 s ? (b) Through what angle has it turned during that time ? (c) Calculate the work done by the torque.

A point A is located on the rim of a wheel of radius R which rolls witout slipping along a horizontal surface witih velocity V. Find the total distance traversed by the point A between successive moments at which it touches the surface.

A particle moves with a constant velocity parallel to the X-axis. Its angular momentum with respect to the originA. Is constantB. Is constantC. Goeson increasingD. Goes on decreasing

The centre of a wheel rolling on a plaen surface moves with a speed `v_0`. A particle on the rim of the wheel at the same level as the centre will be moving at speedA. ZeroB. `v_(0)`C. `sqrt(2)V_(0)`D. `2v_(0)`

A uniform sphere of mass m and radius r rolls without slipping down a inclined plane, inclined at an angle `45^(@)` to the horizontal . Find the magnitude of frictional coefficient at which slipping is absent :A. `(1)/(3)`B. `(2)/(7)`C. `(1)/(5)`D. `(1)/(7)`

A particle is projected at time t=0 from a point P on the ground with a speed `v_0,` at an angle of `45^@` to the horizontal. Find the magnitude and direction of the angular momentum of the particle about P at tiem `t= v_0//g`

Two identical discs are moving with the same kinetic energy. One rolls and the other slides. The ratio of their speeds is:A. `1:1`B. `sqrt(2): sqrt(3)`C. `2:3`D. `1:2`

A ladder of length `5 m` is placed against a smooth wall as shown in figure. The coefficient or friction is `mu` between ladder and ground. What is the minimum value of `mu` , If the ladder is not to slip? A. `mu=(1)/(2)`B. `mu=(1)/(4)`C. `mu=(1)/(3)`D. `mu=(1)/(5)`

A rod of mass m and length l is held vertically on a smooth horizontal floor. Now it is released from this position, find the speed of its centre of mass when it makes an angle `theta` with the vertical.

A block of mass `m` is held fixed against a wall by a applying a horizontal force `F`. Which of the following option is incorrect : .A. frictional force f=mgB. normal reaction N=FC. F will not produce a torqueD. N will not produce any torque