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 as shown in the figure. The magnitude of the acceleration of $A$ and $B$, immediately after the string is cut, are respectively

• A. $g,g$
• B. $g,\frac{g}{2}$
• C. $\frac{g}{2},g$
• D. $\frac{g}{2},\frac{g}{2}$

Answer 1

The correct option is C $\frac{g}{2},g$

FBD of A and B before cutting the string,

For block B
$T=mg$
For block A
$kx=T+2mg$
Since $T=mg$
$\Rightarrow kx=3mg$

Let the acceleration of block A and B be $a_A$ and $a_B$.
For block A,
$kx-2mg=2m{a}_A$
Since $kx=3mg$
$\Rightarrow 3mg-2mg=2m{a}_A$
$\Rightarrow a_A=\frac{g}{2}\uparrow$
For block B,
$mg=m{a}_B$
$\Rightarrow a_B=g\downarrow$