Question

The period of oscillation of a simple pendulum of length \( l \) suspended from the roof of a vehicle which moves down without friction on an inclined plane of inclination \( \theta \), is given by

• A. \( 2 \pi \sqrt{\frac{l}{g \cos \theta}} \)
• B. \( 2 \pi \sqrt{\frac{l}{g \sin \theta}} \)
• C. \( 2 \pi \sqrt{\frac{l}{g \tan \theta}} \)
• D. \( 2 \pi \sqrt{\frac{l}{g}} \)

Hint:

For a pendulum on an inclined plane, the angle \( \theta \) affects the period. Remember to account for the cosine of the angle in the formula for the period.

Answer 1

The Correct Option is A

The period of oscillation of a simple pendulum moving down an inclined plane is given by the formula: \[ T = 2 \pi \sqrt{\frac{l}{g \cos \theta}} \] This formula accounts for the motion of the pendulum on an inclined plane where the effective gravitational force is \( g \cos \theta \).