Two block `A` and `B` of masses `3m` and `m` respectively are connected by a massless and nextensible 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 resectively

Options

A. ` g,(g)/(3)`
B. `(g)/(3),g`
C. `g,g`
D. `(g)/(3),(g)/(3)`

Answer

b

Explanation

Before the string is cut let `x` be the extension in spring as shown in the tension in string Then
`T + 3 mg = kx` …(i)
In `T = mg` ….(ii)
From (i) and (ii), `mg + 3 mg = kx`
or `kx = 4mg`…(iii)
After the string is cut `T = 0`
Let `a_(1)` and `a_(2)` be the accelerations of masses `A` and `B` then
Refer to
`kx - 3mg = 3 mxx a_(1)`
or `a_(1) = (kx -3mg)/(3m) = (4 mg - 3mg)/(3m) = (g)/(3)`
`ma_(2) = mg` or `a_(2) = g` .