Question

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

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

Answer 1

Answer: (B)

$g/2,g$

$\text{Solution}:$

When string is not cut, let $F_s$ be the restoring force within the spring,

For spring B: T=mg

For body A: $F_s=2mg+T=2mg+mg=3mg$

When the string is cut, body B will fall freely therefore, its acceleration is

$a_B=g$

For body A: $\left(2m\right)a_A=F_s-\left(2m\right)g=3mg-2mg=mg$

$\therefore a_A=\frac{g}{2}$

$\text{Hence B is the correct option}$