Assertion:  KE is conserved at every instant of elastic collision. 

Reason:  No deformation of matter occurs in
elastic collision.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

A mass M is tied to the top of two identical poles of height H using massless strings of equal length. The mass is at height h above the ground at equilibrium. If the distance between poles is L the tension in each string will be

• $\frac{\mathrm{Mg} \sqrt{{\left({\displaystyle \frac{\mathrm{L}}{2}}\right)}^2 + {\left( \mathrm{H} - \mathrm{h} \right)}^2}}{2 \left(\mathrm{H} - \mathrm{h}\right)}$

• $\frac{\mathrm{Mg} \sqrt{{\mathrm{L}}^2 + {\mathrm{H}}^2}}{2 \left(\mathrm{H} - \mathrm{h}\right)}$

• $\frac{\mathrm{Mg} \sqrt{{\mathrm{L}}^2 + {\mathrm{H}}^2}}{2 \mathrm{H}}$

• $\frac{\mathrm{Mg} \sqrt{{\mathrm{h}}^2 + {\mathrm{L}}^2}}{2 \mathrm{L}}$

A body is moved in straight line by machine with constant power. The distance travelled by it in time duration t is proportional to

• t^3/2

• t^1/2

• t²

• t

Three bodies, a ring, a solid cylinder and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of the bodies are identical. Which of the bodies reaches the ground with maximum velocity?

• Ring

• Solid cylinder

• Solid sphere

• All reach the ground with same velocity

An air compressor is powered by a 200 rad/s electric motor using a V-belt drive. The motor pulley is 8 cm in radius, and the tension in the V-belt is 135 N on one side and 45 N on the other. The power of the motor will be

• 1.44 kW

• 14.4 kW

• 2.88 kW

• 28.8 kW

A string 0.5 m long is used to whirl a 1 kg stone in a vertical circle at a uniform velocity of 5 m s^-1.  What is the tension in the string when the stone is at the top of the circle?

• 9.8 N

• 30.4 N

• 40.2 N

• 59.8 N

A heavy truck moving with a velocity of 60 km h^-1 collides with a light drum at rest. If the collision be elastic, then the velocity of the drum immediately after collision will be

• zero

• 60 km h^-1

• 120 km h^-1

• uncertain

A steel wire with cross-section 3 cm² has elastic limit 2.4 x 10⁸ N m^-2. The maximum upward acceleration that can be given to a 1200 kg elevator supported by this cable wire if the stress is not to exceed one-third of the elastic limit is (Take g = 10 ms^-2)

• 12 m s^-2

• 10 m s^-2

• 8 m s^-2

• 7 m s^-2

69.

A body of mass 2 kg is thrown up vertically with kinetic energy of 490 J. The height at which the kinetic energy of the body becomes half of its original value is

• 50 m

• 12.25 m

• 25 m

• 10 m

A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubled. The kinetic energy of the system now is

• 2 K

• $\frac{\mathrm{K}}{2}$

• $\frac{\mathrm{K}}{4}$

• 4K