A body sliding on a smooth inclined plane requires 4 seconds to reach the bottom, starting from rest at the top. How much time does it take to cover one-fourth the distance starting from rest at the top?

Options

A. 1 s`
B. ` 2s`
C. ` 4 s`
D. ` 16 s`

Answer

B

Explanation

When a body slides on an inclinde plane, component of weight along the plance produces an acceleration.
`a (ng sin theta)/(m) =g sin theta =Constnt`
If `s` is the length of the inclined plane, then
`s=0(1)/(2) at^(2) =(1)/(2) g sin theta xxt^(2)`
(s')/(s) =(t'^(2))/(t^(2))` or `(s)/(s') =(t^(2))/(t'^(2))`
Given `t=4 s` and `s' =(s)/(4)`
`t'= t sqrt (s')/(s) =4 sqrt (s)/(4s) =(4)/(2) =2 s`.