General
✓✗Find the torque about the origin when a force of \( 3\hat j \) N acts on a particle whose position vector is \( 2\hat k \) m.
- \( 6\hat j \) N m
- \( -6\hat i \) N m
- \( 6\hat k \) N m
- \( 6\hat i \) N m
General
✓✗A disc of mass 2 kg and radius 0.5 m rotates at 4 rad/s about its axis. Its rotational kinetic energy is
- 2 J
- 8 J
- 4 J
- 1 J
General
✓✗A solid cylinder of mass M, length L and radius R. For its moment of inertia about its axis to equal that about a perpendicular axis through its centre, the ratio L/R must be
- \( \sqrt3 \)
- 2
- \( \sqrt2 \)
- 1
General
✓✗The rolling of a body without slipping can be treated as
- oscillation about the point of contact
- pure rotation about the point of contact
- pure rotation about the centre of mass
- pure translation
General
✓✗Three rings, each of mass m and radius r, lie in one plane touching one another, their centres forming an equilateral triangle. The moment of inertia of the system about an axis through the centre of one ring perpendicular to the plane is
- 11mr2
- 9mr2
- 3mr2
- 7mr2
General
✓✗A flywheel of moment of inertia 10 kg m2 is accelerated by a torque of 50 N m from rest. The angle turned in 4 s is
- 80 rad
- 40 rad
- 20 rad
- 10 rad
General
✓✗Two masses of 2 kg and 3 kg hang from the ends of a light string over a pulley of moment of inertia 0.025 kg m2 and radius 0.1 m (no slipping). The acceleration of the masses is (g = 10 m s−2)
- 2 m s−2
- 5 m s−2
- \( \dfrac{10}{7.5} \) m s−2 (about 1.33 m s−2)
- 1 m s−2
General
✓✗A disc of mass 2 kg and radius 0.1 m is rotated by a tangential force of 1 N applied at its rim. Its angular acceleration is
- 1 rad/s2
- 10 rad/s2
- 20 rad/s2
- 5 rad/s2
General
✓✗A solid cylinder of mass 3 kg is rolling on a horizontal surface with velocity 4 m s−1. It collides with a horizontal spring of force constant 200 N m−1. The maximum compression produced in the spring will be
- 0.7 m
- 0.6 m
- 0.5 m
- 0.2 m
General
✓✗The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is I0. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is
- I0 + ML2/2
- I0 + ML2/4
- I0 + 2ML2
- I0 + ML2
General
✓✗A solid homogeneous sphere of mass M and radius R is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of the sphere,
- the angular momentum about the centre of mass is conserved
- the angular momentum of the sphere about the point of contact with the plane is conserved
- the total kinetic energy is conserved
- only the rotational kinetic energy about the centre of mass is conserved
General
✓✗For a rigid body rotating about a fixed axis, all its particles have the same
- angular velocity
- linear velocity
- linear acceleration
- centripetal acceleration
General
✓✗A hollow cylinder rolls down from rest without slipping through a vertical height of 5 m. Its speed at the bottom is (g = 10 m s−2)
- 10 m s−1
- \( \sqrt{50} \) m s−1
- \( \sqrt{75} \) m s−1
- 5 m s−1
General
✓✗A particle moves with constant velocity along a straight line not passing through the origin. The torque on it about the origin is
- decreasing with time
- constant and non-zero
- zero
- increasing with time
General
✓✗A uniform ring of mass M and radius R rolls without slipping with speed v. The kinetic energy of the upper half of the ring relative to the ground is greater than that of the lower half because
- the lower half is at rest
- the upper half has more mass
- points in the upper half move faster than those in the lower half
- the upper half rotates faster