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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Newton's Laws of Motion

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Newton's Laws of Motion

A block A can slide on a frictionless incline of angle θ and length...

A block AA can slide on a frictionless incline of angle θ\theta and length ll, kept inside an elevator travelling up with uniform velocity vv as shown in the figure. Determine the time taken by the block to slide down the length of the incline if it is released from the top.
A block A can slide on a frictionless incline of angle θ and length l , kept inside an elevator travelling up with

Options

  1. A2lg\sqrt{\dfrac{2l}{g}}
  2. Blgsin⁡θ\sqrt{\dfrac{l}{g\sin\theta}}
  3. C2lgcos⁡θ\sqrt{\dfrac{2l}{g\cos\theta}}
  4. D2lgsin⁡θ\sqrt{\dfrac{2l}{g\sin\theta}}

Correct answer

D. 2lgsin⁡θ\sqrt{\dfrac{2l}{g\sin\theta}}

Step-by-step solution

Since the elevator is moving upwards with a uniform velocity vv, its acceleration is zero. Therefore, there is no pseudo force acting on the block, and the effective acceleration due to gravity inside the elevator remains gg.

The component of acceleration of the block along the frictionless incline is a=gsin⁡θa = g \sin \theta.

The block is released from rest, so its initial velocity is u=0u = 0. Let tt be the time taken to slide down the incline of length ll.

Using the second equation of motion, s=ut+12at2s = ut + \dfrac{1}{2}at^2:

l=0+12(gsin⁡θ)t2l = 0 + \dfrac{1}{2}(g \sin \theta)t^2

t2=2lgsin⁡θt^2 = \dfrac{2l}{g \sin \theta}

t=2lgsin⁡θt = \sqrt{\dfrac{2l}{g \sin \theta}}
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