First slide

Application of Newtons laws

Question

The acceleration of block B in the figure will be

Moderate

A

$\frac{m_{2} g}{(4 m_{1} + m_{2})}$
B

$\frac{2 m_{2} g}{(4 m_{1} + m_{2})}$
C

$\frac{2 m_{1} g}{(m_{1} + 4 m_{2})}$
D

$\frac{2 m_{1} g}{(m_{1} + m_{2})}$

Solution

When block m₂moves downward with acceleration a, the acceleration of mass rn I will be 2a because it covers double distance in the same time in comparison to m₂.
Let T be the tension in the string. By drawing the free body diagram of A and B,
$\begin{array}{l} T = m_{1} 2 a . . . . . . . (i) \\ m_{2} g - 2 T = m_{2} a . . . . . . (i i) \end{array}$
By solving (i) and (ii),
$a = \frac{m_{2} g}{(4 m_{1} + m_{2})}$

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