An object takes n times as much time as to slide down a `45^(@)` rough inclined plane it takes to slide down a perfectly smooth inclined plane of the same inslination. The coefficient of kinetic friction between the object and the rough inclied is given by

Options

A. `(1-1/n^2)`
B. `(1/(1-n^2))`
C. `sqrt(1-1/n^2)`
D. `sqrt(1+1/n^2)`

Explanation

`H=ut-(1/2)g t^2`
The maximum height attained by a body vertically projected upward at time ,`t=0` is
`2H= 2ut-g t^2`
`g t^2-2ut-2H=0`
Sum of the roots =`t_1+t^2=(2u)/g` (from equation (1))
`u= ((t_1+t_2)g)/2`
Maximum Height,
`H_max=u^2/2g=(g^2(t_1+t_2)^2)/8`