Direction of Friction
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Q. A solid sphere of mass 2 kg rolls on a smooth horizontal surface at 10 m/s. It then rolls up a smooth inclined plane of inclination 30∘. Height attained by sphere in meter before stopping is: (take g=10 ms−2)
Q. A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?
- Disk
- Depends on their masses
- Sphere
- Both reach at the same time.
Q. A solid sphere of Mass M and radius R is pulled horizontally on a rough surface as shown in the figure. Choose the incorrect alternative(s).
- The magnitude of the frictional force is F/3.
- The frictional force on the sphere acts forward.
- The acceleration of the centre of mass is 2F/3M.
- The acceleration of the centre of mass is 5F/7M.
Q. A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of the vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be:
- 2.0
- 1.2
- 0.1
- 0.4
Q. A horizontal disc rotates freely about a vertical axis through its centre. A ring having the same mass and radius as the disc, is now gently placed on the disc. After some time, the two rotate with a common angular velocity, then
- some friction exists between the disc and the ring
- the angular momentum of the 'disc plus ring' is conserved
- The final common angular velocity is (23)rd of the initial angular velocity of the disc
- (23)rd of the initial kinetic energy changes to heat
Q. A thin ring of mass 2 kg and radius 1 m is rolling without slipping on a horizontal plane with velocity 1 m/s. A small ball of mass 1 kg and moving with velocity 2 m/s in the opposite direction, hits the ring at a height of 1.8 m and goes vertically up with velocity of 1 m/s. Immediately after the collision, which of the following is true?
- Ring undergoes pure rotation about its axis through the centre of mass.
- Ring comes to a complete stop.
- Friction on the ring by the ground is to the left.
- There is no friction between the ring and ground.
Q. Two balls of same mass are projected with the same speed one vertically upwards and the other at angle 60∘ with the vertical. The ratio of their potential energy at the highest point is
- 4 : 1
- 2 : 1
- 3 : 2
- 4 : 3
Q. A uniform disk of mass m and radius R is projected horizontally with velocity V0 on a rough horizontal floor so that it starts off with a purely sliding motion at t = 0. After t0 seconds, it acquires a purely rolling motion as shown in figure.
- Angular momentum of disc at t = 0 about a point on the floor and in the same plane which contains the disc is mV0R.
- Angular momentum of disc at t=t0 about a point on the floor and in the same plane which contains the disc is mV0R.
- Speed of the centre of mass of disc at t=t0 is 2V0/3
- Speed of the centre of mass of disc at t=t0 is 3V0/4