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 Multiple Choice QuestionsMultiple 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

  • ρσ - 1h

  • σρ - 1h

  • 1 - σρh

  • 1 - ρσh


B.

σρ - 1h

Let the volume of the ball = V

Weight of the ball            = Vρg

Upward thrust on ball       = Vσg − Vρg

Now upward acceleration,

   a = Vσg - Vρg = σ - ρρg

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

Then, v2 = 2as = 2 × σ - ρρgh

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

 12 mv2 = mgxor           x = v22g = σ - ρρh = σρ - 1h


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 = 96m / 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

   Net work done (W) =Wg + WT               = 147000 - 117600               = 129400 J           W = 12mvf2 - 12mvi2           W = Kfinal - Kinitial                = 129400 + 12mvf2                = 129400 + 12 × 1000 × 62                = 129400  + 18000                = 147400 J                = 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

As the ball falls to the ground, its potential energy mgh, changes into kinetic energy 12mv12   mgh1 = 12mv12         .....(i)After rebounding, its kinetic energy 12mv22 changes into potential energy mgh2    mgh2 = 12mv22      .... (ii)Dividing Eq. (ii) by Eq. (i), we get      h2h1 = v2v12But  h1 = 2m , e = v2v1 = 0.6 h22m = (0.6)2 = 0.36        h2 = 0.72 m