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In the following arrangement the system is initially at rest. The 5 kg block is now released. Assuming the pulleys and string to be massless and smooth, the acceleration of block C will be

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$\frac{5}{7} m / s^{2}$

$2.5 m / s^{2}$

$\frac{10}{7} m / s^{2}$

answer is D.

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Detailed Solution

Block B will not move.

$\begin{array}{l} 5 g - T = 5 a . . . . . (1) \\ 2 T - 8 g = 8 \frac{a}{2} . . . . . (2) \end{array}$

Solving eqns. (1) and (2), we get

$\begin{array}{l} 2 g = 14 a or a = \frac{g}{7} \\ ∴ \frac{a}{2} = \frac{g}{14} = \frac{10}{14} = \frac{5}{7} m / s^{2} \end{array}$

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