Question

A trolley moves in horizontal direction with an acceleration a. A simple pendulum of length l is suspended from the roof of the trolley. The time period of the pendulum will be

• A. infinity
• B. zero
• C. $2 \pi \sqrt{\frac{l}{(g+a)}}$
• D. $2 \pi \sqrt{\frac{l}{\sqrt{a^{2}+g^{2}}}}$

Answer 1

Answer: (D)

Two accelerations are acting on the bob of pendulum.
(i) Vertically downwards, acceleration $=g$
(ii) Horizontally, due to acceleration of trolley $=a$.
Effective acceleration $=\sqrt{g^{2}+a^{2}} $
$\therefore \,\,\,T=2 \pi \sqrt{\frac{l}{\sqrt{g^{2}+a^{2}}}}$