A simple pendulum of length $L$ is suspended from a ceiling of a car accelerating horizontally with acceleration $a$. What is the time period of small oscillations?

Solution

1. In the frame of the car, there is a pseudo-force $ma$ acting horizontally.
2. The effective acceleration due to gravity is $g_{eff}=\sqrt{g^2+a^2}$.
3. The time period of a simple pendulum is $T=2\pi \sqrt{L/g_{eff}}$.
4. Substituting $g_{eff}$, we get $T=2\pi \sqrt{\frac{L}{\sqrt{g^2+a^2}}}$.
5. Hence the answer is (B).