Two blocks $A$ and $B$ of masses $2 m$ and $m$ respectively are connected by a massless and inextens

Question

Two blocks $A$ and $B$ of masses $2 m$ and $m$ respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring. The magnitudes of acceleration of $A$ and $B$ immediately after the string is cut,  are respectively

Professor PC Thomas Classes · Answer

Before cutting, spring force $kx = 3mg$. Tension $T = mg$. Just after cutting, $T$ becomes zero. For mass $A$ ($2m$), net force is upwards: $kx - 2mg = 3mg - 2mg = mg$. So $a_A = \frac{mg}{2m} = \frac{g}{2}$. For mass $B$ ($m$), only gravity acts downwards: $a_B = g$.