Question

A person measures a time period of a simple pendulum inside a stationary lift and finds it to be T. If the lift starts accelerating upwards with an acceleration `("g"/3)`, the time period of the pendulum will be ______.

Options

• `"T"/sqrt3`

• `sqrt3 "T"/2`

• `sqrt3`T

• `"T"/3`

Answer 1

A person measures a time period of a simple pendulum inside a stationary lift and finds it to be T. If the lift starts accelerating upwards with an acceleration `("g"/3)`, the time period of the pendulum will be `underline(sqrt3 "T"/2)`.

Explanation:

Time period of simple pendulum inside a stationary lift,

T = `2pi sqrt(l/"g")`    ....(i)

where, I = length of string

and g = gravitational acceleration

Acceleration of lift in upward direction.

a = `"g"/3`

∴ Time period of pendulum,

T' = `2pi sqrt(l/("g + a"))`

`= 2pi sqrt(l/("g" + "g"/3))`

`= 2pi sqrt((3l)/(4"g"))`

`= 2pi * sqrt3/2 * sqrt(l/"g")`

`= sqrt3/2 * 2pi sqrt(l/"g")`

`= sqrt3/2 "T"`      ...[from Eq. (1)]