Question

A simple pendulum of length l is suspended from the ceiling of a train which is moving in the horizontal direction with a constant acceleration a. The time period of the pendulum is given by $T=2\pi \sqrt{\frac{l}{g_{eff}}}$ where $g_{eff}$ is given by

• A. g
• B. (g+a)
• C. (g- a)
• D. $\sqrt{g^2+a^2}$

Answer 1

The correct option is D $\sqrt{g^2+a^2}$

There are two perpendicular acceleration vectors; g acting vertically downwards and a acting horizontally. The resultant acceleration is given by
$g_{eff}=\sqrt{g^2+a^2}$
Hence the correct choice is (d)