Question

A simple pendulum is suspended from the ceiling of a car accelerating uniformly on a horizontal road. If the acceleration is $a_0$ and the length of the pendulum is l, find the time period of small oscillations about the mean position.

• A. $2\pi \sqrt{\frac{l}{g}}$
• B. g+a
• C. $2\pi \sqrt{\frac{l}{\sqrt{a^2+g^2}}}$
• D. Particle won't oscillate with fixed time period

Answer 1

The correct option is C

$2\pi \sqrt{\frac{l}{\sqrt{a^2+g^2}}}$

In non-intertial frame bob feels mg downwards and ma${}_{\circ }$ pseudo force backwards.

$\overrightarrow{F}$=Net force $\equiv \sqrt{(m{a}_{\circ }{)}^2+(mg{)}^2}=\overrightarrow{T}=\overrightarrow{F}=m\sqrt{{a_{\circ }}^2+g^2}$

Here$\sqrt{{a_{\circ }}^2+g^2}$ plays the role of effective g

$T=2\pi \sqrt{\frac{l}{g_{eff}}}=2\pi \sqrt{\frac{l}{\sqrt{a^2+g^2}}}$