Question

Two blocks $A$ and $B$ of same mass $m$ connected by a light spring are suspended by an inextensible string as shown in the figure. Find the magnitude of the acceleration of block $A$ and $B$ just after the string is cut.

• A. $2g,0$
• B. $0,2g$
• C. $g,g$
• D. $2g,2g$

Answer 1

The correct option is A $2g,0$

When block $A$ and $B$ are in equilibrium position, let $T_o$ be the spring force and $T$ be the tension in the string.
F.B.D of ${}^{\prime }{B}^{\prime }$

$\begin{array}{}{T}_o=mg& \text{(1)}\end{array}$
F.B.D of ${}^{\prime }{A}^{\prime }$

$T=mg+T_0$
$\begin{array}{}T=2mg& \text{(2)}\end{array}$
When string is cut, tension T becomes zero. but spring does not change its shape just after cutting . So spring force acts on mass $B$.
F.B.D of 'B'

$T_o-mg=m{a}_B$
Since $T_o=mg$ $[$Using $\left(1\right)$$]$
$\Rightarrow a_B=0$

F.B.D of 'A'

$mg+T_o=m.a_A$
$2mg=m.a_A$
$a_A=2g\left(\text{downwards}\right)$