System of Particles and Rotational Motion

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