question_answer

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

A) \[\frac{g.g}{2}\]                                 

B) \[\frac{g}{2},g\]

C) \[g.g\]                          

D) \[\frac{g}{2},\frac{g}{2}\]   

Correct Answer: B

Solution :

When the string is cut, free body diagrams of blocks A and B are shown in the figure \[\therefore \]\[2m{{a}_{A}}=3mg-2mg\] \[{{a}_{A}}=\frac{mg}{2m}=\frac{g}{2}\] Free body diagram of block B shows \[m{{a}_{B}}=mg\] \[\therefore \]    \[{{a}_{B}}=g\] Hence, the correction option is [b].