A simple pendulum of length l and having a bob of mass M is suspended ina 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, what will be its time period ?

Explanation

In this case, the bob of the pendulum is under the action of two accelerations.
(i) Acceleration due to gravitu 'g' acting vertically downwards.
(ii) Centripetal acceleration `a_(c) = (v^(2))/(R)` acting alpng the horizontal direction.
`:.` Effective acceleration, `g' = sqrt(g^(2) +a_(c)^(2))`
or `g' = sqrt(g^(2)+(v^(4))/(R^(2)))`
Now time period, `T' = 2pi sqrt((1)/(g)) = 2pi sqrt((l)/sqrt(g^(2)+(v^(4))/(R^(2))))`