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 acceleration of A and B, immediately after the string is cut, are respectively:

• A. $g,\frac{g}{2}$
• B. $\frac{g}{2},g$
• C. $g,g$
• D. $\frac{g}{2},\frac{g}{2}$

Answer 1

The correct option is B $\frac{g}{2},g$

Before the string is cut, the upward stretching force in the spring is
$kx=3mg$

After the string is cut, the free body diagrams for the two blocks can be shown as in adjacent figure.


For block $A:2m{a}_A=3mg-2mg$
Or $a_A=\frac{g}{2}$

For block B: $m{a}_B=mg$
Or $a_B=g.$