Two identical blocks $A$ and $B$, each of mass $m$ resting on smooth floor, are connected by a light spring…
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
$v \sqrt{\frac{m}{2 k}}$
$m \sqrt{\frac{v}{2 k}}$
$\sqrt{\frac{m v}{k}}$
$\frac{m v}{2 k}$
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, $x=v T=v \times 2 \pi \sqrt{\frac{\mu}{2 k}}$
$\therefore \quad x \propto v \sqrt{\frac{m}{2 k}}$
