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