System of Particles and Rotational Motion

The angular speed of a flywheel is increased from 600 rpm to 1200 rpm in 10 s. The number of revolutions completed by the flywheel during this time is :

1. 600
2. 300
3. 900
4. 150

A thin wire of length 'L' and linear mass density 'm' is bent into a circular ring (in x-y plane) with centre 'C' as shown in figure. The moment of inertia of the ring about an axis yy' will be: [figure]

1. 3mL38
2. 3mL28 2
3. 3mL38 2
4. 3mL28

A thin horizontal disc is rotating about a vertical axis passing through its fixed centre O. Its angular momentum is LA and LB computed about points A and B, respectively, with OB = 2 OA. The value of LALB is: [figure]

1. 2
2. 14
3. 12
4. 1

A solid sphere A of radius R and mass M is attached at a point to a smaller solid sphere B of radius r < R and mass m < M. Assume that the line joining their centres lies along the horizontal. The moment of inertia of the system calculated about a vertical axis passing through the centre of A is IA and that calculated about a vertical axis passing through the centre of B is IB. The difference IA - IB is: [figure]

1. 0
2. (M - m)(R + r)2
3. (m - M)(R + r)2
4. (m - M)(R - r)2

A uniform rod of mass 20 kg and length 5 m leans against a smooth vertical wall making an angle of 60 with it. The other end rests on a rough horizontal floor. The friction force that the floor exerts on the rod is (Take g = 10 m/s2)

1. 200 N
2. 200 3 N
3. 100 N
4. 100 3 N

The Sun rotates around its centre once in 27 days. What will be the period of revolution if the Sun were to expand to twice its present radius without any external influence? Assume the Sun to be a sphere of uniform density.

1. 115 days
2. 108 days
3. 100 days
4. 105 days

A sphere of radius R is cut from a larger solid sphere of radius 2R as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the Y-axis is: [figure]

1. 757
2. 764
3. 78
4. 740

The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is 2400 g cm2. The length of the 400 g rod is nearly:

1. 8.5 cm
2. 17.5 cm
3. 20.7 cm
4. 72.0 cm

A wheel of a bullock cart is rolling on a level road as shown in the figure below. If its linear speed is v in the direction shown, which one of the following options is correct (P and Q are any highest and lowest points on the wheel, respectively)? [figure]

1. Point P moves slower than point Q
2. Point P moves faster than point Q
3. Both the points P and Q move with equal speed
4. Point P has zero speed

The radius of gyration of a solid sphere of mass 5 kg about XY is 5 m as shown in figure. The radius of the sphere is 5x 7 m, then the value of x is: [figure]

1. 5
2. 2
3. 3
4. 5

The ratio of radius of gyration of a solid sphere of mass M and radius R about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is :-

1. 5:3
2. 2:5
3. 5: 3
4. 3: 5

The angular acceleration of a body, moving along the circumference of a circle, is :

1. along the radius towards the centre
2. along the tangent to its position
3. along the axis of rotation
4. along the radius, away from centre

The angular speed of a fly wheel moving with uniform angular acceleration changes from 1200 rpm to 3120 rpm in 16 seconds. The angular acceleration in rad/s2 is

1. 2
2. 4
3. 12
4. 104

Two objects of mass 10 kg and 20 kg respectively are connected to the two ends of a rigid rod of length 10 m with negligible mass. The distance of the center of mass of the system from the 10 kg mass is :

1. 103 m
2. 203 m
3. 10 m
4. 5 m

The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is

1. 2 : 1
2. 2 : 1
3. 4 : 1
4. 1 : 2

An energy of 484 J is spent in increasing the speed of a flywheel from 60 rpm to 360 rpm. The moment of inertia of the flywheel is :

1. 0.07 kg m2
2. 0.7 kg m2
3. 3.22 kg m2
4. 30.8 kg m2

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R). In the light of the above statements, choose the most appropriate answer from the options given below

1. (A) is not correct but (R) is correct
2. Both (A) and (R) are correct and (R) is the correct explanation of (A)
3. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
4. (A) is correct but (R) is not correct

From a circular ring of mass 'M' and radius 'R' an arc corresponding to a 90 sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the center of the ring and perpendicular to the plane of the ring is 'K' times 'MR2'. Then the value of 'K' is :

1. 18
2. 34
3. 78
4. 14

A uniform rod of length 200 cm and mass 500 g is balanced on a wedge placed at 40 cm mark. A mass of 2 kg is suspended from the rod at 20 cm and another unknown mass 'm' is suspended from the rod at 160 cm mark as shown in the figure. Find the value of 'm' such that the rod is in equilibrium. (g = 10 m/s2) [figure]

1. 112 kg
2. 12 kg
3. 13 kg
4. 16 kg

Two particles of mass 5 kg and 10 kg respectively are attached to the two ends of a rigid rod of length 1 m with negligible mass. The centre of mass of the system from the 5 kg particle is nearly at a distance of :

1. 50 cm
2. 67 cm
3. 80 cm
4. 33 cm

Find the torque about the origin when a force of 3 j N acts on a particle whose position vector is 2 k m.

1. 6 j N m
2. -6 i N m
3. 6 k N m
4. 6 i N m

A solid cylinder of mass 2 kg and radius 4 cm is rotating about its axis at the rate of 3 rpm. The torque required to stop after 2 revolutions is :

1. 2 10-3 N m
2. 2 10-6 N m
3. 2 106 N m
4. 12 10-4 N m

A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its centre of mass has speed of 20 cm/s. How much work is needed to stop it?

1. 1 J
2. 2 J
3. 3 J
4. 30 kJ

A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (Kt) as well as rotational kinetic energy (Kr) simultaneously. The ratio Kt : (Kt + Kr) for the sphere is

1. 7 : 10
2. 5 : 7
3. 10 : 7
4. 2 : 5

A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere?

1. Angular velocity
2. Moment of inertia
3. Rotational kinetic energy
4. Angular momentum

Three objects, A : (a solid sphere), B : (a thin circular disk) and C : (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation

1. WC > WB > WA
2. WA > WB > WC
3. WB > WA > WC
4. WA > WC > WB

The moment of the force, F = 4 i + 5 j - 6 k at (2, 0, −3), about the point (2, −2, −2), is given by

1. -8 i - 4 j - 7 k
2. -4 i - j - 8 k
3. -7 i - 8 j - 4 k
4. -7 i - 4 j - 8 k

A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N?

1. 0.25 rad s-2
2. 25 rad s-2
3. 5 m s-2
4. 25 m s-2

Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities 1 and 2. They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is

1. 14I( 1 - 2)2
2. I( 1 - 2)2
3. 18I( 1 - 2)2
4. 12I( 1 + 2)2

Which of the following statements are correct ?

1. A and B only
2. B and C only
3. C and D only
4. B and D only