Question

Two blocks A and B each of mass m are connected by a massless spring of natural length L and spring constant K. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length as shown in figure. A third identical block C also of mass m moves on the floor with a speed v along the line joining A and B and collides elastically with A. Then

• A. The kinetic energy of the A-B system at maximum compression of the spring is zero
• B. The kinetic energy of the A-B system at maximum compression of the spring is
• C. The maximum compression of the spring is
• D. The maximum compression of the spring is

Answer 1

Answer: (B), (D)

The correct options are
B

The kinetic energy of the A-B system at maximum compression of the spring is

D

The maximum compression of the spring is

Let the velocity acquired by A and B be V, then

mv = mV + mV $\Rightarrow V=\frac{v}{2}$

Where x is the maximum compression of the spring. On solving the above equations,

we get x = v ${\left(\frac{m}{2k}\right)}^{\frac{1}{2}}$

At maximum compression, kinetic energy of the

A - B system = $\frac{1}{2}m{V}^2+\frac{1}{2}m{V}^2=m{V}^2=\frac{m{V}^2}{4}$