Question

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

• A. $a_A=2g(\downarrow ),a_B=0$
• B. $a_A=2g(\downarrow ),a_B=g(\downarrow )$
• C. $a_A=2g(\downarrow ),a_B=g(\downarrow )$
• D. $a_A=0,a_B=g(\downarrow )$

Answer 1

The correct option is A $a_A=2g(\downarrow ),a_B=0$

When block $A$ and $B$ are in equilibrium position
Let spring force be $T_0$ and tension in string be $T$.

FBD of B
FBD of A
When string is cut, tension $T$ becomes zero. But spring does not change its shape after cutting. So same spring force $T_0$ acts on mass $B$,

After cutting the string, FBD of $B$
FBD of $A$