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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

In the arrangement depicted in the figure, both springs are...

In the arrangement depicted in the figure, both springs are unstretched. If the block is given a displacement of xx and released, what will be its initial acceleration?
In the arrangement depicted in the figure, both springs are unstretched. If the block is given a displacement of x and

Options

  1. A(k1+k2)xm\dfrac{(k_1 + k_2)x}{m} opposite to the displacement
  2. Bk1k2x(k1+k2)m\dfrac{k_1 k_2 x}{(k_1 + k_2)m} opposite to the displacement
  3. C∣k1−k2∣xm\dfrac{|k_1 - k_2|x}{m} opposite to the displacement
  4. D(k1+k2)xm\dfrac{(k_1 + k_2)x}{m} along the displacement

Correct answer

A. (k1+k2)xm\dfrac{(k_1 + k_2)x}{m} opposite to the displacement

Step-by-step solution

When the block is displaced by a distance xx from its equilibrium position, one spring gets stretched by xx and the other gets compressed by xx.

The restoring force from the first spring is F1=k1xF_1 = k_1 x in the direction opposite to the displacement.

The restoring force from the second spring is F2=k2xF_2 = k_2 x, also in the direction opposite to the displacement.

The net restoring force acting on the block is:
Fnet=F1+F2=k1x+k2x=(k1+k2)xF_{net} = F_1 + F_2 = k_1 x + k_2 x = (k_1 + k_2)x

This net force acts opposite to the direction of displacement.

Using Newton's second law, the initial acceleration aa of the block is:
a=Fnetm=(k1+k2)xma = \dfrac{F_{net}}{m} = \dfrac{(k_1 + k_2)x}{m}

The direction of the acceleration is opposite to the displacement.
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