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# Work, Energy and Power

#### Multiple Choice Questions

141.

A wooden ball of density ρ is immersed in water of density σ to depth h and then released, then the height x above the surface of water upto which the ball jumps out of water is equal to

B.

Let the volume of the ball = V

Weight of the ball            = Vρg

Upward thrust on ball       = Vσg − Vρg

Now upward acceleration,

Let v be the velocity of the ball while reaching the surface of water, after being released at depth h in water.

Then,

For the motion of the ball outside the water, KE at the surface of water = PE at height x

142.

Assertion:  Power of a engine depends on mass, angular speed, torque and angular momentum, then the formula of power is not derived with the help of dimensional method.

Reason:  In mechanics, if a particular quantity depends on more than three quantities, then we can not derive the formula of the quantity by the help of dimensional method.

• 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.

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

The assertion is correct as we cant derive formula with help of dimensional analysis if quantity depends on more than 3 quantities, here power depends on 4 quantities we cant derive its formula by dimensional method.

143.

A lift of mass 1000 kg is descending with a speed of 6 ms-1 . Suddenly the cable of the lift begins to slip and it falls with a constant acceleration a = $\frac{9}{6}$m / s2 . What is the kinetic energy of the lift after falling a distance 15 m ?

• 121.3 kJ

• 155.6 kJ

• 147.4 kJ

• 134.1 kJ

C.

147.4 kJ

144.

A ball is dropped to the ground from a height of 2 m. The coefficient of restitution is 0.6. To what height will the ball rebound ?

• 0.41 m

• 0.9 m

• 0.72 m

• 0.28 m

C.

0.72 m