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

• A

  $g,\frac{g}{3}$
• Correct answer
  B

  $\frac{g}{3}, g$
• C

  $g, g$
• D

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

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 $a=\frac{\mathrm{mg}}{\mathrm{m}}=g\downarrow$.

Hence, the correct answer is option: 'B'.