Question

A simple pendulum of length L and having a bob of mass m is suspended in a car. The car is moving on a circular track of radius R with a uniform speed v. If the pendulum makes small oscillations in a radial direction about its equilibrium position, its time period of oscillation is

• A. $\mathrm { T } = 2 \pi \sqrt { \frac { \mathrm { L } } { \mathrm { g } } }$
• B.
• C.
• D. $\mathrm { T } = 2 \pi \sqrt { \frac { \mathrm { L } } { \mathrm { g } ^ { 2 } - \frac { v ^ { 4 } } { \mathrm { R } ^ { 2 } } } }$

Answer 1

Answer: (B)

Answer 2

the bob of the pendulum has two accelerations

(i) Centripetal acceleration

Its acts horizontally.

(ii) Acceleration due to gravity = g. it acts vertically

Downwards

The effective acceleration due to gravity,

$\therefore$ Time period