Question

A seconds pendulum is suspended in a car that is traveling with a constant speed of $10m/s$ round a circle of radius $10m$. If the pendulum undergoes small oscillations, the time period will be

• A. $2s$
• B. $4s$
• C. greater than $2s$ but less than $4s$
• D. less than $2s$

Answer 1

Answer: (D)

The time period of a second pendulum is $2s$. When it is rotated in a circle, a centripetal acceleration also acts on pendulum towards center. So, the effective acceleration due to gravity $g^{\prime }$ increases to $\sqrt{g^2+a^2}$, and we know that $T\propto \frac{1}{\sqrt{g^{\prime }}}$, So the time period of the pendulum will decrease, i.e., time period will be less than 2 s.