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A block of mass $m$ is placed on top of a block of mass $2 m$ which in turn is placed on a fixed horizontal surface. The coefficient of friction between all surface is $μ = 1 .$ A mass less string is connected to each mass and wraps half way around a mass less and friction less pulley as shown. The pulley is pulled by horizontal force of magnitude $F = 6 m g$ towards right as shown in figure. The magnitude of acceleration of pulley is __.

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$5 m / s^{2}$

$\frac{25}{2} m / s^{2}$

$20 m / s^{2}$

$25 m / s^{2}$

answer is A.

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Detailed Solution

$3 m g - m g = m a_{1}$

$a_{1} = 2 g = 20 m / s^{2}$

$3 m g + m g - 3 m g = 2 m a_{2}$

$a_{2} = 5 m / s^{2}$

$T a_{1} + T a_{2} - 2 T a_{p} = 0$

$a_{p} = \frac{a_{1} + a_{2}}{2} = \frac{20 + 5}{2} = \frac{25}{2} m / s^{2}$

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