Q.
A and B are fixed points and the mass M is tied by strings at A and B. If the mass M is displaced slightly out of this plane and released, it will execute oscillations with period ( given $AM = BM = L,AB = 2d$)
A) $2\sqrt{\frac{L}{g}}\pi$
B) $2\pi\sqrt{\frac{\left( L^{2} - d^{2} \right)^{1/2}}{g}}$
C) $2\pi\sqrt{\frac{\left( L^{2} + d^{2} \right)^{1/2}}{g}}$
D) $2\pi\sqrt{\frac{\left( 2d^{2} \right)^{3/2}}{g}}$
Explanation
(b) The motion of $M$ is SHM, with length $CM = \sqrt{L^{2} - d^{2}}$
$\therefore\ \ \ \ 2\pi\sqrt{\frac{\left( L^{2} + d^{2} \right)^{1/2}}{g}}$
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Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.