question_answer

Two blocks A and B of masses 3 m and m respectively are connected by a massless and inextensible string. The whole system is suspended by massless spring as shown in figure.                             The magnitudes of acceleration of A and B immediately after the string is cut, are respectively:

A) \[\frac{g}{3},g\] 

B) \[~g,\text{ }g\]

C) \[\frac{g}{3},\frac{g}{3}\]  

D) \[g,\frac{g}{3}\]

Correct Answer: A

Solution :

[a] Before cutting the string \[kx=T+3\text{ mg         }...\text{(i)}\] \[\text{T=mg                    }...\text{(ii)}\] \[\Rightarrow \text{kx=4mg}\] After cutting the string \[T=0\] \[{{a}_{A}}=\frac{4mg-3mg}{3m}\] \[{{a}_{A}}=\frac{g}{3}\uparrow \text{  and  }{{a}_{B}}=\frac{mg}{m}=g\downarrow \]