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Two blocks A ...

Question

Two blocks A and B of same mass $m$ attached with a light string are suspended by a spring as shown in the figure. Find the acceleration of block A and B just after the string is cut.

A

a_{A} = g (↓), a_{B} = g (↑)

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B

a_{A} = g (↑), a_{B} = g (↓)

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C

a_{A} = \frac{g}{2} (↑) a_{B} = g (↓)

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D

a_{A} = \frac{3}{2} g (↑), a_{B} = \frac{3}{2} g (↓)

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Solution

The correct option is B $a_{A} = g (↑), a_{B} = g (↓)$
When string is not cut:
FBD of $A$ block
$k x = m g + T$
FBD of $B$ block
$T = m g$
$\Rightarrow k x = 2 m g$
When string is cut:
FBD of A block
$k x - m g = m a_{A}$
$2 m g - m g = m a_{A}$
$= a_{A} = g (u p w a r d s)$
FBD of B block
$m a_{B} = m g$
$a_{B} = g (d o w n w a r d s)$

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