A pendulum is hanging from the ceiling of a car having an acceleration $a_{0}$ with respect to the road. find the angle made by the string with the vertical.

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Solution

With the car frame of reference, a pseudo force $m . a_{o}$ must be applied so the equation of horizontal equilibrium is
$m . a_{o} = T . sin x . . . . (1)$

where,
m=mass of the bob of pendulum
T=tension in the string
x=angle made by the string with vertical
equation of vertical equilibrium is

$m g = T . cos x . . . . . . (2)$

Diving (1) by (2), we get

$\frac{T . sin x}{T . cos x} = \frac{m . a_{o}}{m . g}$

$tan x = \frac{a_{o}}{g}$

Hence,
$x = {tan}^{- 1} (\frac{a_{o}}{g})$

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A pendulum is hanging from the ceiling of a car having an acceleration a0 with respect to the road. find the angle made by the string with the vertical.

A pendulum is hanging from the ceiling of a car having an acceleration $a_{0}$ with respect to the road. find the angle made by the string with the vertical.