Q.
In the given figure four identical spheres of equal mass $m$ are suspended by wires of equal length $l_{0}$, so that all spheres are almost touching to each other. If the sphere 1 is released from the horizontal position and all collisions are elastic, the velocity of sphere 4 just after collision is
A) $\sqrt{2gl_{0}}$
B) $\sqrt{3gl_{0}}$
C) $\sqrt{gl_{0}}$
D) $\sqrt{\frac{gl_{0}}{2}}$
Explanation
(a) When the sphere 1 is released from horizontal position, then from energy conservation, potential energy at height $l_{0} =$ kinetic energy at bottom
Or $mgl_{0} = \frac{1}{2}mv^{2}$
Or $v = \sqrt{2gl_{0}}$
Since, all collisions are elastic, so velocity of sphere 1 is transferred to sphere 2, then from 2 to 3 and finally from 3 to 4. Hence, just after collision, the sphere 4 attains a velocity equal to $\sqrt{2gl_{0}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.