Q. A mass M is suspended from a light spring. An additional mass m added displaces the spring further by a distance x. Now the combined mass will oscillate on the spring with period
A) $T = 2\pi\sqrt{\frac{mg}{X(M + m)}}$
B) $T = 2\pi\sqrt{\frac{(M + m)X}{mg}}$
C) $T = \pi/2\sqrt{\frac{mg}{X(M + m)}}$
D) $T = 2\pi\sqrt{\frac{(M + m)}{mg}}$
Explanation
(b) A total restoring force, $F = kX = mg$
Or $k = \frac{mg}{X}$
Total mass that oscillates$= (M + m)$
$\therefore\ \ \ T = 2\pi\sqrt{\frac{(M + m)}{mg/X}} = 2\pi\sqrt{\frac{(M + m)X}{mg}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.