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

Options

A. `g, g//2`
B. `g//2,g`
C. `g,g`
D. `g//2, g//2`

Answer

B

Explanation

When string is not cut, let `F_(s)` be the restoring force within the spring
For spring B: `T=mg`
For body A: `F_(s)=2mg+T=2mg+mg=3mg`
When the string is cut, body B will fall freely therefore, its acceleration is `a_(B)=g`
For body A: `(2m)a_(A)=F_(s)-(2m)g=3mg-2mg=mg`
`:. a_(A)=g/2`