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.A. `2 pi sqrt (L)/(g cos prop)`B. `2 pi sqrt (L)/(s sin prop)`C. `2 pi sqrt(L)/(g)`D. `2 pi sqrt(L)/(g tan prop)`

The period of oscillation of a simple pendulum of length (L) suspended

1.	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.A. `2 pi sqrt (L)/(g cos prop)`B. `2 pi sqrt (L)/(s sin prop)`C. `2 pi sqrt(L)/(g)`D. `2 pi sqrt(L)/(g tan prop)`
Answer» Correct Answer - A<br>As shown in the figure,`g sin prop` is the pseudo acceleration applied by the observer in the accelerated frame.<br> `a_x = g sin prop cos prop`<br> `a_y = g = g sin^2 prop = g(1 - sin^2 prop)= g cos^2 prop`<br> `a = sqrt(a_x^2 + a_y^2)`<br> =`sqrt(g^2 sin^2 prop cos^2 prop + g^2 cos^4 prop)`<br> = `g cos prop sqrt(sin^2 prop + cos^2 prop = g cos prop)`<br> :. `T = 2 pi sqrt(L)/(g cos prop)`.