Application of Newtons laws

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Question

In the previous question surface is replaced by block C of mass m as shown in the figure. In this case the acceleration of block B is found to be $\frac{3 F}{n m} m / s^{2}$ . The value of n is _________.

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Solution

$Constrain equation 2 a + 3 b + c$ ……(1)
$\begin{array}{l} F - 2 T = 2 m a . . . . . . (2) \\ T = m c . . . . . . . . . (3) \\ 3 T = 4 m b . . . . . . . (4) \end{array}$
$On solving above four equation b = \frac{3 F}{21 m} m / s^{2}$

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