System of Particles and Rotational Motion · Question 13

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