Two identical blocks $A$ and $B$, each of mass $m$ resting on smooth floor, are connected by a light spring of natural length $L$ and the spring constant $k$, with the spring at its natural length. $A$ third identical block $C$ (mass $m$ ) moving with a speed $(v)$ along the line joining $A$ and $B$ collides with $A$. The maximum compression in the spring is proportional to

• Correct answer
  A

  $v \sqrt{\frac{m}{2 k}}$
• B

  $m \sqrt{\frac{v}{2 k}}$
• C

  $\sqrt{\frac{m v}{k}}$
• D

  $\frac{m v}{2 k}$

Solution

When block $(C)$ strikes the block $(A)$, then it begins to oscillate, whose time period $T=2 \pi \sqrt{\frac{m}{2 k}}$
Compression, $x=v T=v \times 2 \pi \sqrt{\frac{\mu}{2 k}}$ $\therefore \quad x \propto v \sqrt{\frac{m}{2 k}}$

Hence, the correct answer is option: 'A'.