1. A simple pendulum hanging freely and at rest is vertical because in that position ___________
a) Kinetic energy is zero
b) Potential energy is zero
c) Kinetic energy is minimum
d) Potential energy is minimum
Explanation: In the position of equilibrium, the potential energy of the simple pendulum is minimum. Therefore a simple pendulum hanging freely and at rest is vertical because in that position potential energy is minimum.
2. A bullet is fired and gets embedded in a block kept on the table. If a table is frictionless, then ___________
a) Kinetic energy gets conserved
b) Potential energy gets conserved
c) Momentum gets conserved
d) Kinetic energy and potential energy gets conserved
Explanation: Only momentum gets conserved when a bullet is fired and gets embedded in a block kept on a frictionless table. Some kinetic energy is lost when the bullet penetrates the block.
3. A ball moves in a frictionless inclined table without slipping. The work done by the table surface on the ball is ___________
a) Positive
b) Negative
c) Zero
d) Infinity
Explanation: Motion without slipping implies pure rolling. During pure rolling work done by friction force is zero.
4. Assertion: When a body moves along a circular path, no work is done by the centripetal force.
Reason: The centripetal force is used on moving the body along the circular path and hence no work is done.
a) Both assertion and reason are true and reason is the correct explanation of the assertion
b) Both assertion and reason are true but the reason is not the correct explanation of assertion
c) Assertion is true but reason is false
d) Both assertion and reason are false
Explanation: The assertion is true but the reason is false. The work done by the centripetal force is zero because it acts perpendicular to the circular path.
5. A flywheel has a mass of 25kg has a radius of 0.2m. What force should be applied tangentially to the rim of the flywheel so that it acquires an angular acceleration of 2rad/s2?
a) 2N
b) 5N
c) 3N
d) 1N
Explanation: M = 25kg, R = 0.2m, α = 2rad/s2
Moment of inertia of the flywheel about its axis,
I = 1/2 MR2=1/2×25×0.22=0.5kgm2
As torque, τ = F×R=I×α
Therefore, Force F = Iα/R=(0.5×2)/0.2=5N.
6. The angular momentum of a body is 3.14 is and its rate of revolution is 10 cycles per second. Calculate the moment of inertia of the body about the axis of rotation.
a) 5 kgm2
b) 0
c) 31.4 kgm2
d) 0.5 kgm2
Explanation: L = 3.14 Js v = 10 rps
ω=2πv=2×3.14×10/rad
As L = Iω
I = L/ω = 3.14/(2×3.14×10)=0.5kgm2.
7. The angular velocity of a planet revolving in an elliptical orbit around the sun increases, when it comes closer to the sun. This is due to ______________
a) Conservation of momentum
b) Newton’s second law of motion
c) Conservation of angular momentum
d) Law of angular velocity
Explanation: The angular velocity of a planet revolving in an elliptic orbit around the sun increases when it comes closer to the sun increases when it comes closer to the sun because its moment of inertia about the axis through the sun decreases. When it goes far away from the sun, its moment of inertia decreases so as to conserve angular momentum.
8. In a hand driven grinding machine, the handle is put _____________
a) Perpendicular to the stone
b) Near the circumference of the stone
c) A few distances above the stone
d) As far away from the stone
Explanation: For a given force, torque can be increased if the perpendicular distance of the point of application of the force from the axis of rotation is increased. Hence the handle put near the circumference produces maximum torque.
9. A faulty balance with unequal arms has its beam horizontal. The weights of the two pans are _____________
a) Equal
b) Unequal
c) Uncertain
d) Very large
Explanation: They are of unequal mass. Their masses are in the inverse ratio of the arms of the balance.
10. Which part of the ship is made heavy?
a) The whole ship should be light in weight
b) The top part
c) The bottom part
d) The sides
Explanation: The bottom of the ship is made heavy so that the centre of gravity remains low. This ensures the stability of its equilibrium.