First slide

Pseudo force

Question

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

Moderate

A

$2 π \sqrt{\frac{l}{g \cos α}}$
B

$2 π \sqrt{\frac{l}{g}}$
C

$2 π \sqrt{\frac{l}{g \sin α}}$
D

$2 π \sqrt{\frac{l}{g \tan α}}$

Solution

Since, the vehicle is moving down the plane with an acceleration $g \sin α$ and the bob will experience a pseudo force up along the plane mg sin $α$
effective acceleration of the pendulum is g cos $α$
The period of oscillation of the pendulum,
$T = 2 π \sqrt{\frac{l}{g'}} = 2 π \sqrt{\frac{l}{g \cos α}}$

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