Question

Two blocks $1$ and $2$ of masses $2m$ and $m$ are suspended by means of a massless spring and a massless inextensible string as shown in the figure. The acceleration of blocks $1$ and $2$ immediately after the string is cut are respectively.

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

Answer 1

The correct option is B $g\uparrow ,\frac{g}{2}\downarrow$

Just before the string in cut, force on the spring pulling $up=kx=3mg$

Therefore after string is cut, free body diagram of block $A$

$\begin{array}{c}\therefore 2m{a}_A=3mg-2mg\\ or{a}_A=\frac{mg}{2m}=\frac{g}{2}\\ FreebodydiagramofblockB\\ \therefore m{a}_B=mg\\ or{a}_B=g\end{array}$