Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively
To solve the problem of finding the acceleration of blocks A and B immediately after the string is cut, we follow these steps:
Step 1: Analyzing the system before the string is cut
Initially, blocks A and B are connected and suspended by a spring. The forces on each block are balanced as they are stationary.
Step 2: Analyzing block A after the string is cut
Once the string is cut, block B falls freely under gravity. Therefore, the tension in the string is removed, and we only need to consider the mass 3m for block A.
The net force on block A is due to gravity:
F_A = 3mg
The resulting acceleration a_A of block A is given by:
a_A = \dfrac{F_A}{3m} = \dfrac{3mg}{3m} = g
Step 3: Analyzing block B after the string is cut
Block B is now in free fall, meaning the only force acting on it is gravity:
F_B = mg
The resulting acceleration a_B of block B is given by:
a_B = \dfrac{F_B}{m} = \dfrac{mg}{m} = g
Since the mass m of block B has no other forces acting upon it, apart from gravity, it experiences the full acceleration due to gravity.
Conclusion:
Therefore, the accelerations of blocks A and B immediately after the string is cut are:
