Q. 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 at $C$ (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
A) $v\sqrt{\frac{m}{2k}}$
B) $m\sqrt{\frac{v}{2k}}$
C) $\sqrt{\frac{mv}{k}}$
D) $\frac{mv}{2k}$
Explanation
(a) When block $(C)$ strikes the block $(A)$, then it begins to oscillate, whose time period
$T = 2\pi\sqrt{\frac{m}{2k}}$
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Compression $x = vT = v \times 2\pi\sqrt{\frac{m}{2k}}$
$\therefore$ $x \propto v\sqrt{\frac{m}{2k}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.