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Two blocks of masses $m = 5 kg$ and $M = 10 kg$ are connected by a string passing over a pulley B as shown. Another string connects the center of pulley B to the floor and passes over another pulley A as shown. An upward force F is applied at the center of pulley A. Both the pulleys are massless. Find the acceleration of blocks m and M, if F is $500 N$ (Take $g = 10 m / s^{2}$ )

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$4 m / s^{2}, 5 m / s^{2}$

$6 m / s^{2}, 5 m / s^{2}$

$10 m / s^{2}, 5 m / s^{2}$

$15 m / s^{2}, 2.5 m / s^{2}$

answer is D.

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Detailed Solution

on Let $T_{0} =$ tension in the string passing over A

T= tension in the string passing over B

$2 T_{0} = F and 2 T = T_{0} T = F / 4$

$T = F / 4 = 125 N$ As $T > m g$ and $M g$ both the blocks will accelerate upwards. Acceleration of m,

$a_{1} = \frac{T - m g}{m} = \frac{125 - 50}{5} = 15 m / s^{2}$

Acceleration of M,

$a_{2} = \frac{T - M g}{M} = \frac{125 - 100}{10} = 2.5 m / s^{2}$

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