The period of oscillation of a simple pendulum of length (L) suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination (prop), is given by.

Options

A. `2pisqrt((L)/(gcosalpha))`
B. `2pisqrt((L)/(gsinalpha))`
C. `2pisqrt((L)/(g))`
D. `2pisqrt((L)/(g tanalpha))`

Answer

A

Explanation

Free body diagram of bob of the pendulum with respect to the accelerating frame of reference is as follows :

`:.` Net force on the bob is
`F_("net") = mg cos alpha` (figure b)
or
Net acclerating of the bob is
`g_(eff) = g cos alpha`
`T = 2pisqrt((L)/(g_(eff)))`
`rArr t = 2pisqrt((L)/(gcosalpha))`