A cabin is moving in a gravity free space along y-axis with an acceleration a. What is the time period of oscillation of a particle of mass m attached with an inextensible string of length l, in this cabin

Options

A. `2pi sqrt((l)/(g))`
B. `2pi sqrt((l)/(a))`
C. `2pi sqrt((l)/(a + g))`
D. `2pi sqrt((l)/(g-a))`

Answer

B

Explanation

In gravity free space g = 0
Tension in the string at equilibrium position =ma
Effective g = a
And thus `T = 2pi sqrt((l)/(a))`
Hence (B) is correct