Two blocks A and B of masses 3 m and m respectively are connected by a massless and inextensible string. The…

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

1. $g,\frac{g}{3}$
2. $\frac{g}{3}, g$
3. $g, g$
4. $\frac{g}{3},\frac{g}{3}$

Solution

Before the string is cut, tension is acting in the string in downward position.
$kx=T+3mg$ ......(i)
$T=mg$ ......(ii)

$\Rightarrow kx=4mg$
After the string is cut, $T=0$

$a=\frac{kx-3mg}{3m}$
$a=\frac{\mathrm{4m}g-3mg}{3m}$
Acceleration of $A$is $a=\frac{g}{3}\uparrow$ and acceleration of $B$ is $a=\frac{\mathrm{mg}}{\mathrm{m}}=g\downarrow$.

Asked in: NEET 2017

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