Question

Two blocks $A$ and $B$ of mass $M$ and $2M$ respectively, are hanging from a ceiling by means of a massless spring and a light string as shown. If the string between the blocks is suddenly cut and the downward acceleration is taken positive, then what will be the acceleration of the block $A$ and $B$?

• A. $g,2g$
• B. $2g,g$
• C. $-2g,g$
• D. $2g,-g$

Answer 1

The correct option is C $-2g,g$

Let $T_o$ and $T$ be the spring force and tension in the string.
From the FBD of the system, before the spring is cut.

For block B,
$\begin{array}{}T=2mg& \text{(1)}\end{array}$
For block A,
$T_o=T+mg$
$\begin{array}{}{T}_o=3mg& \text{(2)}\end{array}$
Now if string is cut, block B will be falling freely
$\therefore a_B=g$
From the FBD of block A,

$\Rightarrow M{a}_A=Mg-T_o$
Since $T_o=3mg$
$M{a}_A=-2Mg$
$a_A=-2g$ (Upwards)