Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, a

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Solution

Q.
Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively [2017]

1 $\frac{g}{3}, g$

2 $g, g$

3 $\frac{g}{3}, \frac{g}{3}$

4 $g, \frac{g}{3}$

Ans.
(1)

Before the string is cut

$k x = T + 3 m g$ ...(i)

$T = m g$ ...(ii)

From eqns. (i) and (ii)

$k x = 4 m g$

Just after the string is cut

$T = 0$

$a_{A} = \frac{k x - 3 m g}{3 m}$

$a_{A} = \frac{4 m g - 3 m g}{3 m} = \frac{m g}{3 m} = \frac{g}{3}$

and $a_{B} = g$

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