553 + Interview Questions in ROTATIONAL-MOTION IN GENERAL AWARENESS Page 1 InterviewSolution

1.	A solid cylinder and a sphere, having the same mass, rolls without slipping with the same linear velocity. If the kinetic energy of the cylinder is `75 J`, that of the sphere must beA. `60 J`B. `70 J`C. `80 J`D. `90 J`
Answer» Cylinder : `(1+(k^(2))/(R^(2)))(1)/(2)mv^(2)=(1+(1)/(2))(1)/(2)mv^(2)=(3)/(4)mv^(2)=75J` Sphere : `(1+(2)/(5))(1)/(2)mv^(2)=(7)/(10)mv^(2)=(7)/(10)(100)=70J`

Discussion

2.	The M.I. of solid sphere of mass M and radius R about its diameter isA. `(2)/(5) MR^(2)`B. `(7)/(5)MR^(2)`C. `(2)/(3)MR^(2)`D. `(5)/(3)MR^(2)`
Answer» Correct Answer - A

Discussion

3.	If a solid sphere of mass 500 gram rolls without slipping with a velocity of 20 cm/s, then the rolling kinetic energy of the sphere will beA. 140 JB. 280 JC. 0.014 JD. 0.028 J
Answer» Correct Answer - C `K.E. = (1)/(2)mv^(2)(1+(K^(2))/(R^(2)))`

Discussion

4.	If I is the M.I. of a solid sphere about an axis parallel to a diameter of the sphere and at a distance x from it, which of following graphs represents the variation of I with xA. B. C. D.
Answer» Correct Answer - D `I = m K^(2)`

Discussion

5.	A disc is rotaing with an angular velocity `omega_(0)`. A constant retarding torque is applied on it to stop the disc. The angular velocity becomes `(omega_(0))/(2)` after n rotations. How many more rotations will it make before coming to rest ?A. nB. 2nC. `(n)/(2)`D. `(n)/(3)`
Answer» Correct Answer - D

Discussion

6.	The M.I. of a solid cylinder about its axis is I. It is allowed to rool down an incline plane without slipping. If its angular velocity at the bottom be `omega`, then kinetic energy of rolling cylinder will beA. `I omega^(2)`B. `(3)/(2)I omega^(2)`C. `2 I omega^(2)`D. `(1)/(2)I omega^(2)`
Answer» Correct Answer - B `K E_("Roll")=(1)/(2)I omega^(2)+(1)/(2)mv^(2)=(1)/(2)I omega^(2)+(1)/(2) mr^(2)omega^(2)` `= (1)/(2) I omega^(2)+I Omega^(2)=(3)/(2)I omega^(2)`

Discussion

7.	If a disc of mass 400 gm is rolling on a horizontal surface with uniform speed of 2 m/s, then its rolling kinetic energy will beA. 0.12 JB. 1.2 JC. 120 JD. 12 J
Answer» Correct Answer - B `KE_("rolling")=(1)/(2)mv^(2)(1+(K^(2))/(R^(2)))`

Discussion

8.	A rigid and a disc of different masses are rotating with the same kinetic energy. If we apply a retarding torque `tau` on the ring, it stops after making n revolution. After how many revolutions will the disc stop, if the retarding torque on it is also `tau` ?A. nB. 2nC. 4nD. n/2
Answer» Correct Answer - A Workdone = Change in KE `= tau theta` = Constant As `tau` is same in the two cases, `theta` must be same i.e. number of revolutions must be same.

Discussion

9.	If the torque acting on a system is zero then, which of the followin quantities is conserced ?A. linear momentumB. angular momentumC. moment of inertiaD. angular velocity
Answer» Correct Answer - B

Discussion

10.	The dimensions of torque are :A. `[L^(3)M^(0)T^(-2)]`B. `[L^(2)M^(2)T^(-3)]`C. `[L^(2)M^(1)T^(-2)]`D. `[L^(2)M^(-1)T^(-3)]`
Answer» Correct Answer - C

Discussion

11.	A torque of 50 Nm acts on a rotating body for 5 s. Its angular momentum isA. increases by 250 kg `m^(2)//s`B. increases by 10 kg `m^(2)//s`C. increases by 55 kg `m^(2)//s`D. decreases by 250 kg `m^(2)//s`
Answer» Correct Answer - A `(d l)/(dt) = tau therefore d l = tau dt`

Discussion

12.	A solid sphere of mass 2 kg and radius 5 cm is rotating at the rate of 300 rpm. The torque required to stop it in `2pi` revolutions isA. `2.5 xx 10^(4) `dyne cmB. `2.5xx10^(-4)` dyne cmC. `2.5xx 10^(6)` dyne cmD. `2.5xx10^(5)` dyne cm
Answer» Correct Answer - D In one revolution angle discribed is `2 pi` `therefore 2pi` revolution corresponds to `4 pi^(2)`. `tau = I alpha = ((2)/(5)MR^(2))((omega_(2)^(2)-omega_(1)^(2))/(2theta))` `= (2)/(5)xx2xx25xx10^(-4)xx(4pi^(2)(0-25))/(2xx4pi^(2))` `= 2.5xx10^(-2)Nm`. `= 2.5xx10^(-2)xx10^(7)` dyne cm.

Discussion

13.	If the resultant external torque acting on a body is zero, then angular momentum of the bodyA. changesB. remains constantC. is infinityD. zero
Answer» Correct Answer - B

Discussion

14.	When same torque acts on two rotating rigid bodies to stop them, which have same angular momentum,A. body with greater moment of inertia stops firstB. body with smaller moment of inertia stops firstC. both the bodies will be stopped after the same timeD. we can not predict which stops first
Answer» Correct Answer - C

Discussion

15.	The relation between the torque `tau` and angular momentum L of a body of moment of inertia I rotating with angular velocity `omega` isA. `tau = dL//dt`B. `tau = L.omega`C. `tau = dL//d omega`D. `tau = L xx omega`
Answer» Correct Answer - A

Discussion

16.	Consider a system of two particles having masses `m_(1)` and `m_(2)`. If the particle of mass `m_(1)` is pushed towards the centre of mass of particles through a distance `d`, by what distance would the particle of mass `m_(2)` move so as to keep the mass centre of particles at the original position?A. `m_(1)/(m_(1)+m_(2)) d`B. `m_(1)/m_(2) d`C. `d`D. `m_(2)/m_(1) d`
Answer» Correct Answer - b

Discussion

17.	A homogeneous rod of mass 3 kg is pushed along the smooth horizontal surface by a horizontal suface by a horizontal force F equal to 40 N. The angle `theta` for which rod hasd pure translation motion is `(g=10 m//s^(2))`A. `45^(@)`B. `37^(@)`C. `53^(@)`D. `60^(@)`
Answer» Correct Answer - B

Discussion

18.	A ring and a disc having the same mass, roll without slipping with the same linear velocity. If the kinetic energy of the ring is 8 j , Find the kinetic energy of disc (in J)A. 2 JB. 4 JC. 6 JD. 12 J
Answer» Correct Answer - C `(KE_("disc"))/(KE_("ring"))=(1+(K^(2)//R^(2))_(d))/(1+(K^(2)//R^(2))_(r ))=(1+(1)/(2))/(1+1)=((3)/(2))/(2)` `KE_("disc")=(3)/(4)xx KE_("ring")` `= (3)/(4)xx(2)/(8) = 6 J`.

Discussion

19.	A ring and a disc having the same mass, roll without slipping with the same linear velocity. If the kinetic energy of the ring is 8 j , Find the kinetic energy of disc (in J)
Answer» Correct Answer - 6

Discussion

20.	A disc can roll wihtout slippingg, without applying any external force on aA. rough inclined planeB. smooth inclined planeC. rough horizontal surfaceD. smooth horizontal surface
Answer» Correct Answer - A::C::D

Discussion

21.	Consider the situation shown in the figure. Uniform rod of length L can rotat freely about the hinge A in vertical plane. Pulleys and stringa are light and frictionless. If the rod remains horizontal at rest when the system is released then the mass of the rod is A. `(4)/(3)M`B. `(8)/(3)M`C. `(16)/(3) M`D. `(32)/(3)M`
Answer» Correct Answer - C

Discussion

22.	A rod of mass `M = 5kg` and length `L = 1.5 m` is held vertical on a table as shown. A gentle push is given to it and it starts falling. Friction is large enough to prevent end A from slipping on the table. (a) Find the sum of linear momentum of all the particles of the rod when it rotates through an angle `theta = 37^(@)` (b) Find the friction force and normal reaction force by the table on the rod, when `theta = 37^(@)` (c) Find value of angle q when the friction force becomes zero. `[tan 37^(@) = (3)/(4) " and " g = 10 m//s]`
Answer» Correct Answer - (a) `7.5 kg m//s` (b) `f = 9 N, N = 24.5 N` (c) `cos^(-1) ((2)/(3))`

Discussion

23.	A rod of mass M and length l is suspended freely from its endandit canoscillate in the vertical plane about the point of suspension. It is pulled to one side and then released. It passes through the equilibrium position withangular speed `omega` . What is the kinetic energy while passing through the mean position ?A. `(Ml^(2)omega^(2))/(2)`B. `(Ml^(2) omega^(2))/(6)`C. `(Ml^(2)omega^(2))/(4)`D. `(Ml^(2)omega^(2))/(8)`
Answer» Correct Answer - B `KE =(1)/(2)I omega^(2)=(1)/(2)(M l^(2)omega^(2))/(3)=(M l^(2)omega^(2))/(6)`

Discussion

24.	The end B of the rod AB which makes angle `theta` with the floor is being pulled with a constant velocity `v_(0)` as shown. The length of the rod is l. At the instant when `theta=37^(@)` A. velocity of end A is `(4)/(3)v_(0)` downwardsB. angular velocity of rod is `(5)/(3)(v_(0))/(l)`C. angular velocity of rod is constantD. velocity of end A is constant
Answer» Correct Answer - A::B::D

Discussion

25.	According to the principle of conservation of angular momentum, if moment of inertia of a rotating body decreases, then its angular velocityA. decreasesB. increasesC. remains constantD. becomes zero
Answer» Correct Answer - B

Discussion

26.	If the angular velocity of a rotating rigid body is increased then its moment of inertia about that axisA. increasesB. decreasesC. becomes zeroD. remains unchanged
Answer» Correct Answer - D

Discussion

27.	A ring of mass `m` and radius `r` is melted and then moulded into a sphere. The moment of inertia of the sphere will beA. more than that of the ringB. less than that of the ringC. equal to that of the ringD. the information given is incomplete
Answer» Correct Answer - B

Discussion

28.	A uniform rod of mass `M` and length `L` is hinged at its end. The rod is released from its vertical position by slightly pushing it. What is the reaction at the hinge when the rod becomes horizontal, again vertical.
Answer» Correct Answer - (a) More time (b) `(sqrt21 - 3)/(6)`

Discussion

29.	One end of a uniform rod of length l and mass m is hinged at A. It is released from the rest from horizontal position AB as shown in figure. The force exerted by the rod on the hinge when it becomes verticle is A. `3/2mg`B. `5/2mg`C. `3mg`D. 5mg
Answer» Correct Answer - B

Discussion

30.	Two particles each of mass m are attached at end points of a massless rod AB of length l. Rod is hinged at point C as shown. Rod is released from rest from horizontal position. At the instant when rod reaches its vertical position as shown, which of the following is / are correct: A. Speed of the particle at B is thrice the speed of particle at AB. Net force on particle B is `(6mg)/(5)`C. Angular acceleration of the system is zero.D. Both x and y components of hinge force are non-zero
Answer» Correct Answer - A::B::C

Discussion

31.	The moment of inertia of a body about a given axis is `1.2 kg m^(2)`. Initially, the body is at rest. In order to produce a rotational `KE` of `1500 J`, for how much duration, an acceleration of `25 rad s^(-2)` must be applied about that axis ?A. ` 4 s`B. ` 2 s`C. ` 8 s`D. ` 10 s`
Answer» `K=(1)/(2)I omega^(2)implies 1500=(1)/(2)xx1.2xxomega^(2)` `omega=50 rad//s=omega_(0)+alpha timplies 50=25timplies t=2 s`

Discussion

32.	A uniform circular disc of mass 1.5 kg and raius 0.5 m is initially ar rest on a horiozntal frictonless surface. Three forces of equal matgnitude F = 0.5 N are applied simultaneously along the three sides of an equilateral triangle XYZ with its vertices on the perimeter of the disc (see figure). One second after applying the forces the angular speed of the disc in `rad s^(-1)` is
Answer» Correct Answer - B `3[(Fxxrxx(1)/(2)] = I alpha` `3xx 0.5xx0.5 xx(1)/(2) = (1)/(2)xx1.5xx0.5xx0.5xxalpha` `rArr alpha =2 rads^(-1)` `omega = omega_0 +alphat rArr omega =0+2xx1= rads^(-1)`

Discussion

33.	A thin but very large plank of mass 2 m is placed on a horziontal smooth surface. A solid cylinder of mass m and radius r is given only translational velocity `v_(0)` and gently placed on the plank as shown in the figure. The coefficient of kinetic friciton between the plank and the cylinder is `mu`.
Answer» Correct Answer - (A)Q,(B)S,(C)P,(D)R

Discussion

34.	A flat horizontal belt is running at a constant speed V. There is a uniform solid cylinder of mass M which can rotate freely about an axle passing through its centre and parallel to its length. Holding the axle parallel to the width of the belt, the cylinder is lowered on to the belt. The cylinder begins to rotate about its axle and eventually stops slipping. The cylinder is, however, not allowed to move forward by keeping its axle fixed. Assume that the moment of inertia of the cylinder about its axle is `(1)/(2) MR^(2)` where M is its mass and R its radius and also assume that the belt continues to move at constant speed. No vertical force is applied on the axle of the cylinder while holding it. (a) Calculate the extra power that the motor driving the belt has to spend while the cylinder gains rotational speed. Assume coefficient of friction `= mu`. (b) Prove that `50%` of the extra work done by the motor after the cylinder is placed over it, is dissipated as heat due to friction between the belt and the cylinder
Answer» Correct Answer - (a) `P = mu m g. V`

Discussion

35.	Calculate the radius of gyration of a cylindrical rod of mass M and length L about an axis of rotation perpendicular to its length and passing through its centre.
Answer» Correct Answer - `K=L//sqrt(12)`

Discussion

36.	AB and CD are two indential rods each of length L and mass M joined to from a cross. Find the M.L of the system about a bisector of the angel between the rods (XY): A. `(ml^(2))/(6)`B. `(ml^(2))/(3)`C. `(ml^(2))/(12)`D. `(2ml^(2))/(3)`
Answer» Correct Answer - C

Discussion

37.	A string of negligible thicknes is wrapped several times around a cylinder kept on a rough horizontal surface. A man standing at a distance l from the cylinder holds one end of the sitting an pulls the cylinder towards him figure. There is no slipping anywhere. The length of the string passed through the hand of the man whicle the cylinder reaches his hands is A. `L`B. `2L`C. `3L`D. `4L`
Answer» Velocity of the highest point `= 2` (velocity of center)

Discussion

38.	A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is `k`. If radius of the ball be `R`, then the fraction of total energy associated with its rotation will be.A. `(k^(2))/(R^(2))`B. `(k^(2))/(k^(2)+R^(2))`C. `(R^(2))/(k^(2)+R^(2))`D. `(k^(2)+R^(2))/(R^(2))`
Answer» `(K_(g))/(K)=((1)/(2)mv^(2)xx(k^(2))/(R^(2)))/((1)/(2)mv^(2)(1+(k^(2))/(R^(2))))=(k^(2))/(k^(2)+R^(2))`

Discussion

39.	A rod of mass m and length l in placed on a smooth table. An another particle of same mass m strikes the rod with velocity `v_(0)` in a direction perpendicular to the rod at distance `x( lt l//2)` from its centre . Particle sticks to the end. Let `omega` be the angular speed of system after collision , then As x is increased from 0 to l/2 , the angular speed `omega`.A. will continuously increaseB. will continuously decreaseC. will first increase and then decreaseD. will first increase and then decrease
Answer» Correct Answer - C

Discussion

40.	A rod of mass m and length l in placed on a smooth table. An another particle of same mass m strikes the rod with velocity `v_(0)` in a direction perpendicular to the rod at distance `x( lt l//2)` from its centre . Particle sticks to the end. Let `omega` be the angular speed of system after collision , then Find the maximum possible value of impulse (by varying x) that can be imparted to the particle during collision. Particle still sticks to the rod.A. `(mv_(0))/(2)`B. `(2mv_(0))/(3)`C. `(3mv_(0))/(4)`D. `(4mv_(0))/(5)`
Answer» Correct Answer - A

Discussion

41.	A disc of mass M and radius R is rotating with angular velocity `omega_(0)` about a vertical axis passing through its centre (O). A man of mass `(M)/(2)` and height `(R)/(2)` is standing on the periphery. The man gradually lies down on the disc such that his head is at a distance `(R)/(2)` from the centre and his feet touching the edge of the disc. For simplicity assume that the man can be modelled as a thin rod of length `(R)/(2)`. Calculate the angular speed `(omega)` of the platform after the man lies down.
Answer» Correct Answer - `omega = (24)/(19) omega_(0)`

Discussion

42.	A disc and a solid sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first ?A. SphereB. Both reach at the same timeC. Depends on their massesD. Disc
Answer» Correct Answer - a

Discussion

43.	A solid sphere, disc and solid cylinder, all of the same mass, are allowed to roll down (from rest) on inclined plane, themA. solid sphere reaches the bottom firstB. solid sphere reaches the bottom lateC. disc will reach the bottom firstD. all of them reach the bottom at the same time
Answer» Time to reach at the bottom `t=sqrt((2h)/(g))xx(1)/(sintheta)xxsqrt(1+k^(2)//R^(2))` `t` is minimum for solid sphere

Discussion

44.	A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum accelerraton down the plane is for (no rolling)A. solid sphereB. hollow sphereC. ringD. all same.
Answer» Correct Answer - D (d) This is a case of slidding (the plane frictionless) and therefore the acceleration of all the bodies is same `(g sin theta).`

Discussion

45.	A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling)A. solid sphereB. hollow sphereC. ringD. all same
Answer» Correct Answer - `a= g sin theta`

Discussion

46.	A convex surface has a uniform radius of curvature equal to 5R. A wheel of radius R is rolling without sliding on it with a constant speed `v`. Find the acceleration of the point (P) of the wheel which is in contact with the convex surface.
Answer» Correct Answer - `(5v^(2))/(6R)`

Discussion

47.	A disc of radius R is rolling without sliding on a horizontal surface at a constant speed of `v` (a) What is speed of points A and B on the vertical diameter of the disc ? Given `AB = (R)/(2)` (b) After what time, for the first time, speed of point A becomes equal to present speed (i.e., the speed at the instant shown in the figure) of point B?
Answer» Correct Answer - (a) `V_(A) = 2V, V_(B) = (3V)/(2)` (b) `t = (2R)/(V) cos^(-1) ((3)/(4))`

Discussion

48.	A uniform ring of mass m and radius R is released from top of an inclined plane. The plane makes an angle `theta` with horizontal. The cofficent of friction between the ring and plane is `mu`. Initially, the point of contact of ring and plane is P. Angular momentum of ring about an axis passing from point P and perpendicular to plane of motion as a function of time t isA. `mgR(sintheta)t-mumgR(costheta)t`B. `mgR(sintheta)t`C. `mgR(sintheta)t+mumgR(costheta)t`D. `mgR(1-mu^(2))(sintheta)t`
Answer» Correct Answer - B

Discussion

49.	A wheel ios rolling without sliding on a horizontal surface. The centre of the wheelk moves with a constant speed `v_(0)`. Consider a point P on the rim which is at the top at time t=0. The square of speed of point P is plooted against time t. The correct plot is (R is radius of the wheel)A. B. C. D.
Answer» Correct Answer - B

Discussion

50.	A block with a square base measuring `axxa` and height h, is placed on an inclined plane. The coefficient of friction is `mu`. The angle of inclination `(theta)` of the plane is gradually increased. The block will A. topple before sliding if `mu gt (a)/(h)`B. topple before sliding if `mu lt (a)/(h)`C. slide before toppling if `mugt(a)/(h)`D. slide before toppling if `mugt(a)/(h)`
Answer» Correct Answer - A::D

Discussion

Explore topic-wise InterviewSolutions in .

A solid cylinder and a sphere, having the same mass, rolls without slipping with the same linear velocity. If the kinetic energy of the cylinder is `75 J`, that of the sphere must beA. `60 J`B. `70 J`C. `80 J`D. `90 J`

The M.I. of solid sphere of mass M and radius R about its diameter isA. `(2)/(5) MR^(2)`B. `(7)/(5)MR^(2)`C. `(2)/(3)MR^(2)`D. `(5)/(3)MR^(2)`

If a solid sphere of mass 500 gram rolls without slipping with a velocity of 20 cm/s, then the rolling kinetic energy of the sphere will beA. 140 JB. 280 JC. 0.014 JD. 0.028 J

If I is the M.I. of a solid sphere about an axis parallel to a diameter of the sphere and at a distance x from it, which of following graphs represents the variation of I with xA. B. C. D.

A disc is rotaing with an angular velocity `omega_(0)`. A constant retarding torque is applied on it to stop the disc. The angular velocity becomes `(omega_(0))/(2)` after n rotations. How many more rotations will it make before coming to rest ?A. nB. 2nC. `(n)/(2)`D. `(n)/(3)`

The M.I. of a solid cylinder about its axis is I. It is allowed to rool down an incline plane without slipping. If its angular velocity at the bottom be `omega`, then kinetic energy of rolling cylinder will beA. `I omega^(2)`B. `(3)/(2)I omega^(2)`C. `2 I omega^(2)`D. `(1)/(2)I omega^(2)`

If a disc of mass 400 gm is rolling on a horizontal surface with uniform speed of 2 m/s, then its rolling kinetic energy will beA. 0.12 JB. 1.2 JC. 120 JD. 12 J

A rigid and a disc of different masses are rotating with the same kinetic energy. If we apply a retarding torque `tau` on the ring, it stops after making n revolution. After how many revolutions will the disc stop, if the retarding torque on it is also `tau` ?A. nB. 2nC. 4nD. n/2

If the torque acting on a system is zero then, which of the followin quantities is conserced ?A. linear momentumB. angular momentumC. moment of inertiaD. angular velocity

The dimensions of torque are :A. `[L^(3)M^(0)T^(-2)]`B. `[L^(2)M^(2)T^(-3)]`C. `[L^(2)M^(1)T^(-2)]`D. `[L^(2)M^(-1)T^(-3)]`

A torque of 50 Nm acts on a rotating body for 5 s. Its angular momentum isA. increases by 250 kg `m^(2)//s`B. increases by 10 kg `m^(2)//s`C. increases by 55 kg `m^(2)//s`D. decreases by 250 kg `m^(2)//s`

A solid sphere of mass 2 kg and radius 5 cm is rotating at the rate of 300 rpm. The torque required to stop it in `2pi` revolutions isA. `2.5 xx 10^(4) `dyne cmB. `2.5xx10^(-4)` dyne cmC. `2.5xx 10^(6)` dyne cmD. `2.5xx10^(5)` dyne cm

If the resultant external torque acting on a body is zero, then angular momentum of the bodyA. changesB. remains constantC. is infinityD. zero

When same torque acts on two rotating rigid bodies to stop them, which have same angular momentum,A. body with greater moment of inertia stops firstB. body with smaller moment of inertia stops firstC. both the bodies will be stopped after the same timeD. we can not predict which stops first

The relation between the torque `tau` and angular momentum L of a body of moment of inertia I rotating with angular velocity `omega` isA. `tau = dL//dt`B. `tau = L.omega`C. `tau = dL//d omega`D. `tau = L xx omega`

A homogeneous rod of mass 3 kg is pushed along the smooth horizontal surface by a horizontal suface by a horizontal force F equal to 40 N. The angle `theta` for which rod hasd pure translation motion is `(g=10 m//s^(2))`A. `45^(@)`B. `37^(@)`C. `53^(@)`D. `60^(@)`

A ring and a disc having the same mass, roll without slipping with the same linear velocity. If the kinetic energy of the ring is 8 j , Find the kinetic energy of disc (in J)A. 2 JB. 4 JC. 6 JD. 12 J

A ring and a disc having the same mass, roll without slipping with the same linear velocity. If the kinetic energy of the ring is 8 j , Find the kinetic energy of disc (in J)

A disc can roll wihtout slippingg, without applying any external force on aA. rough inclined planeB. smooth inclined planeC. rough horizontal surfaceD. smooth horizontal surface

According to the principle of conservation of angular momentum, if moment of inertia of a rotating body decreases, then its angular velocityA. decreasesB. increasesC. remains constantD. becomes zero

If the angular velocity of a rotating rigid body is increased then its moment of inertia about that axisA. increasesB. decreasesC. becomes zeroD. remains unchanged

A ring of mass `m` and radius `r` is melted and then moulded into a sphere. The moment of inertia of the sphere will beA. more than that of the ringB. less than that of the ringC. equal to that of the ringD. the information given is incomplete

A uniform rod of mass `M` and length `L` is hinged at its end. The rod is released from its vertical position by slightly pushing it. What is the reaction at the hinge when the rod becomes horizontal, again vertical.

One end of a uniform rod of length l and mass m is hinged at A. It is released from the rest from horizontal position AB as shown in figure. The force exerted by the rod on the hinge when it becomes verticle is A. `3/2mg`B. `5/2mg`C. `3mg`D. 5mg

The moment of inertia of a body about a given axis is `1.2 kg m^(2)`. Initially, the body is at rest. In order to produce a rotational `KE` of `1500 J`, for how much duration, an acceleration of `25 rad s^(-2)` must be applied about that axis ?A. ` 4 s`B. ` 2 s`C. ` 8 s`D. ` 10 s`

Calculate the radius of gyration of a cylindrical rod of mass M and length L about an axis of rotation perpendicular to its length and passing through its centre.

AB and CD are two indential rods each of length L and mass M joined to from a cross. Find the M.L of the system about a bisector of the angel between the rods (XY): A. `(ml^(2))/(6)`B. `(ml^(2))/(3)`C. `(ml^(2))/(12)`D. `(2ml^(2))/(3)`

A disc and a solid sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first ?A. SphereB. Both reach at the same timeC. Depends on their massesD. Disc

A solid sphere, disc and solid cylinder, all of the same mass, are allowed to roll down (from rest) on inclined plane, themA. solid sphere reaches the bottom firstB. solid sphere reaches the bottom lateC. disc will reach the bottom firstD. all of them reach the bottom at the same time

A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum accelerraton down the plane is for (no rolling)A. solid sphereB. hollow sphereC. ringD. all same.

A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling)A. solid sphereB. hollow sphereC. ringD. all same

A convex surface has a uniform radius of curvature equal to 5R. A wheel of radius R is rolling without sliding on it with a constant speed `v`. Find the acceleration of the point (P) of the wheel which is in contact with the convex surface.