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, g/2
(B)g/2,g✓ Correct
(C)g , g
(D)g/2,g/2
Answer: (B)
Solution
Before the string is cut, the spring supports the total weight (2m+m)g=3mg, so the spring force is Fs=3mg.
Immediately after the string is cut:
Block B (mass m) is free and falls with acceleration aB=g (free fall).
Block A (mass 2m) still has the spring force Fs=3mg acting upward and weight 2mg downward.
Net upward force on A: Fnet=3mg−2mg=mg
Acceleration of A: aA=2mmg=2g (upward)
Therefore, the magnitudes are g/2 and g respectively, which is option (B).