Question

in the system shown ma=mb=mc=m . All surfaces are smooth and string is ideal . If the system is released from rest, then find the acceleration of c
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Answer 1

The acceleration of C is g/2

Explanation:

The figure is attached

If the tension in the string is T and in the frame of reference of C if the acceleration of the block A is a downwards then

$m_Ag-T=m_Aa$

And $T=m_Ba$

Thus,

$m_Ag-m_Ba=m_Aa$

$\implies mg-ma=ma$

$\implies a=\frac{g}{2}$

Since block A can only go downwards

Therefore, if the block B moves with a displacement x in the left direction,

block C will move with a displacement x in the right direction so that the centre of mass is at its initial position

Therefore,

$x_C=x_B=x$

Differentiating twice

$\frac{d^2x_C}{dt^2}=\frac{d^2x_B}{dt^2}$

$\implies a_C=\frac{g}{2}$

Hope this answer is helpful.

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