Two rectangular blocks A and B of masses 2 ~kg and 3 ~kg respectively are connected by a spring of spring constant 10.8 Nm ⁻¹ and are placed on a frictionless horizontal surface. The block A was given an initial velocity of 0.15 ~ms ⁻¹ in the direction shown in the figure. The maximum compression of the spring during the motion is

Step-by-step solution

As the block A moves with velocity 0.15 ~ms ⁻¹ , it compresses thespring which pushes B towards right. A goes on compressing the spring till the velocity acquired by B becomes equal to the velocity of A , ie, 0.15 ~ms ⁻¹ . Let this velocity be v. Now, spring is in a state of maximum compression. Let x be the maximum compression at this stage. According to the law of conservation of linear momentum, we get or aligned m _ A u &= ( m _ A + m _ B ) v v &= m _ A u m _ A + m _ B &= 2 0.15 2+3 =0.06 ~ms ⁻¹ aligned Accordi