Block `A` of mass` M = 2 kg` is connected to another block `B` of mass `m= 1 kg` with a string and a spring of force constant `k = 600 N//m` as shown in Fig. Initially, spring is compressed to `10 cm` and whole system is moving on a smooth surface with a velocity `v = 1 m//s`. At any time, thread is burnt, the velocity of block `A`, when `B` is having maximum velocity w.r.t. ground, is

Options

A. zero
B. `1m//S`
C. `3m//s`
D. none of these

Answer

C

Explanation

The velocity of `B` will be maximum when spring comes to its natural length. Let at the at time their velocities are `v_(1)` and `v_(2)` as shown

Conservation of momentum,
`2v_(1)+1v_(2)(2+1)xx1implies2v_(1)+v_(2)=3`…..i
Conservation of energy
`1/22v_(1)^(2)+1/21v_(2)^(2)=1/2600(10/100)^(2)=1/23(1)^(2)implies2v_(1)^(2)+v_(2)^(2)=9`
From eqn i and ii
`v_(1)=2m//s, v_(2)=-1m//s` or `v_(1)=0, v_(2)=3m//s`
The second solution is possible.