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Q. Two blocks are arranged as shown in figure. Assuming the surfaces and the pulleys $P_{1}$ and $P_{2}$ are all smooth and pulleys and string are light, if the acceleration of the block $B$ is found to be $\frac{n F}{17 m} m / s ^{2}$ 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 $a=\frac{n F}{21 m} m / s ^{2}$. The value of $n$ is___.Physics Question Image

Laws of Motion

Solution:

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