Question

in the system ma = mb= mc =m. All the surfaces are smooth and string is ideal if the system is released from rest then find the acceleration of c​

Answer 1

Answer:

g/2 is the correct option

Answer 2

The acceleration of c is g/2

Therefore, option (2) is correct.

Explanation:

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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