Question

A block of mass $m$ is projected with velocity $u$ forwards another identical block with has a massless spring attached to its face. The spring constant of the spring is $k$ and blocks are on smooth horizontal surface. Maximum compression in the spring is:

• A. $u\sqrt{\frac{2m}{k}}$
• B. $u\sqrt{\frac{m}{k}}$
• C. $u\sqrt{\frac{m}{2k}}$
• D. $u\sqrt{\frac{m}{4k}}$

Answer 1

The correct option is B $u\sqrt{\frac{m}{k}}$

By conservation of energy

$\frac{1}{2}m{u}^2=\frac{1}{2}k{x}^2$

$x=u\sqrt{\frac{m}{k}}$