In the given figure mass of block A is m and that B is 2m. They are attached at the ends of spring and kept on horizontal surface. Now the spring is compressed by $x_{0}$ and released. Find displacement of block B by the time compression of the spring is reduced to $\frac{x_{0}}{2} .$ Assume both are slipping in opposite directions together.

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$\frac{x_{0}}{4}$

$\frac{x_{0}}{3}$

$\frac{x_{0}}{6}$

$\frac{x_{0}}{2}$

answer is C.

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Detailed Solution

Since net force on the system of two blocks is zero.
$x_{A} + x_{B} = \frac{x_{0}}{2}$
$m x_{A} = 2 m x_{B}$
$\Rightarrow x_{B} = \frac{x_{0}}{6}$

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