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 person is standing in an elevator. In which situation he finds himself weightless?

• Elevator is going up with constant speed.

• Elevator is moving down with constant speed.

• Elevator is accelerating up with g.

• Elevator is accelerating down with g.

3.

The displacement of a body is given to be proportional to the cube of time elapsed. The magnitude of the acceleration of the body is proportional to

• $\sqrt{\mathrm{t}}$

• t

• t²

• t^3/2

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

The radii of circular paths of two particles of same mass are in ratio 6 : 8 then what will be velocities ratio if they have a constant centripetal force?

• $\sqrt{3} : 4$

• $4 : \sqrt{3}$

• $2 : \sqrt{3}$

• $\sqrt{3} : 2$

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

Assertion:  Use of ball bearing between two moving parts of a machine is a common practice. 

Reason:  Ball bearing reduces rolling friction and provides good stability.

• 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.

Assertion:  A judo fighter in order to throw his opponent on to the mat tries to initially bend his opponent and then rotate him around his hip. 

Reason:  As the mass of opponent is brought closer to the fighter's hip, the force required to throw the opponent is reduced.

• 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.