The acceleration of block B in the figure will be Options: A . &nbspm2g(4m1+m2) B . &nbsp2m2g(4m1+m2) C . &nbsp2m1g(m1+4m2) D . &nbsp2m1g(m1+m2)

The acceleration of block B in the figure will be

Question

The acceleration of block B in the figure will be

Options:

A . m2g(4m1+m2)

B . 2m2g(4m1+m2)

C . 2m1g(m1+4m2)

D . 2m1g(m1+m2)

Answer: Option A
:
A
When the block

m_{2}

moves downward with acceleration a, the acceleration of mass

m_{1}

will be 2a because it covers double distance in the same time in comparison to

m_{2}

.
Let T is the tension in the string.
By drawing the free body diagram of A and B

T = m_{1} 2 a - - - - - - - - - - (i)

M_{2} g ­ - 2 T = m_{2} a - - - - - - - - - - - (i i)

By solving (i) and (ii)
By solving (i) and (ii)

a = \frac{m_{2} g}{(4 m_{1} + m_{2})}

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