General
✓✗A wheel having moment of inertia 2 kg m2 about its vertical axis rotates at the rate of 60 rpm about this axis. The torque which can stop the wheel's rotation in one minute would be
- \( \dfrac{\pi}{18} \) N m
- \( \dfrac{\pi}{15} \) N m
- \( \dfrac{2\pi}{15} \) N m
- \( \dfrac{\pi}{12} \) N m
General
✓✗Statement I: When a cat falls and lands on its feet, its total angular momentum about its centre of mass remains zero.
Statement II: Gravity exerts no torque about the centre of mass of a body.
Statement II: Gravity exerts no torque about the centre of mass of a body.
- Both Statement I and Statement II are correct
- Both Statement I and Statement II are incorrect
- Statement I is correct but Statement II is incorrect
- Statement I is incorrect but Statement II is correct
General
✓✗A uniform rod AB of length l and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A is ml2/3, the initial angular acceleration of the rod will be
- \( \dfrac{2g}{3l} \)
- \( \dfrac{mgl}{2} \)
- \( \dfrac{3g}{2l} \)
- \( \dfrac32gl \)
General
✓✗Four particles of mass 1 kg each are placed at the corners of a square of side 2 m. The moment of inertia about an axis through the centre perpendicular to the plane of the square is
- 4 kg m2
- 8 kg m2
- 2 kg m2
- 16 kg m2
General
✓✗A wheel of a bullock cart is rolling on a level road with linear speed v. P and Q are the highest and lowest points on the wheel respectively. Which of the following is correct?
- Point P has zero speed.
- Both the points P and Q move with equal speed.
- Point P moves slower than point Q.
- Point P moves faster than point Q.
General
✓✗Statement I: The angular momentum of a particle moving in a straight line with constant velocity about any point is constant.
Statement II: No torque acts on a particle with zero net force.
Statement II: No torque acts on a particle with zero net force.
- Both Statement I and Statement II are correct
- Both Statement I and Statement II are incorrect
- Statement I is correct but Statement II is incorrect
- Statement I is incorrect but Statement II is correct
General
✓✗A wheel starting from rest has a constant angular acceleration of 2 rad/s2. Its angular velocity after 5 s is
- 25 rad/s
- 2.5 rad/s
- 10 rad/s
- 7 rad/s
General
✓✗The centre of mass of a system of two particles is nearer to
- the lighter particle
- the faster particle
- neither; it is always at the midpoint
- the heavier particle
General
✓✗Statement I: A particle moving in a straight line can have non-zero angular momentum about a point.
Statement II: Angular momentum is defined only for rotating bodies.
Statement II: Angular momentum is defined only for rotating bodies.
- Both Statement I and Statement II are correct
- Both Statement I and Statement II are incorrect
- Statement I is correct but Statement II is incorrect
- Statement I is incorrect but Statement II is correct
General
✓✗A torque of 20 N m acts on a wheel of moment of inertia 4 kg m2 initially at rest. Its angular velocity after 3 s is
- 60 rad/s
- 5 rad/s
- 15 rad/s
- 12 rad/s
General
✓✗A projectile of mass 4 kg breaks into two pieces of 1 kg and 3 kg at the top of its path. Both pieces land at the same time. The 1 kg piece lands 30 m beyond the point where the projectile would have landed, and the projectile would have landed 60 m from the launch point. The 3 kg piece lands at a distance from the launch point of
- 70 m
- 50 m
- 40 m
- 60 m
General
✓✗A solid sphere and a hollow sphere of the same mass and radius roll without slipping with the same speed. The ratio of their total kinetic energies (solid : hollow) is
- 21 : 25
- 3 : 5
- 25 : 21
- 1 : 1
General
✓✗The centre of mass of a uniform circular ring lies
- at its centre, where there is no mass
- on the ring
- at a point on the ring nearest to the ground
- anywhere on the diameter
General
✓✗A flywheel slowed by a constant frictional torque loses half its angular speed in 10 s. The further time it takes to stop, and the fraction of its initial kinetic energy still left at the 10 s mark, are
- 10 s and 1/4
- 10 s and 1/2
- 5 s and 1/2
- 20 s and 1/4
General
✓✗A wheel rolls without slipping. The ratio of the speeds of the point at the top to the point at the end of a horizontal radius is
- 2 : 1
- 1 : 1
- \( 1 : \sqrt2 \)
- \( \sqrt2 : 1 \)