First slide

Connected bodies

Question

Two blocks A and B of masses 2m and m, respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring with the block A above block B . The magnitudes of acceleration of A and B immediately after the string is cut, are respectively:

Moderate

A

g, $\frac{g}{2}$
B

$\frac{g}{2}$ , g
C

g, g
D

$\frac{g}{2}$ , $\frac{g}{2}$

Solution

After string is cut, free body diagram of block A gives
$2 {ma}_{A} = 3 mg - 2 mg or a_{A} = \frac{mg}{2 m} = \frac{g}{2}$
Free body diagram of block B gives
${ma}_{B} = mg or a_{B} = g$

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