The trollet car having simple pendulum decelerated by friction. In consequence, the pendulum has time period `T`. If `T_(o)` is time period of the simple pendulum in the absence of any acceleration of the trolley car, the value of `(T)/(T_(o))` is---

Explanation

`T = 2pi sqrt((l)/(sqrt(a^(2)+g^(2)))) , a = mug, T = 2pi sqrt((l)/(gsqrt(mu^(2)+1)))`
`T = T_(o) = sqrt((1)/(sqrt(mu^(2)+1)))rArr(T)/(T_(o)) = (1)/((mu^(2)+1)(1)/(4))`