Starting form rest, a body slides down a `45^(@)` inclined plane in twice the time it takes to slide down the same distance in the absence of friction. The coefficient of friction between the body and the inclined plane is

Options

A. 0.75
B. 0.33
C. 0.25
D. `0.80`

Answer

A

Explanation

Let acceleration if `I^(st)` case is `a_(1)` and that in second case is `a_(2)`
Now, `1/2a_(1)t^(2)=1/2a_(2)(2t)^(2)rArr a_(2)=(a_(1))/4`....(i)
Clearly, `a_(1)=(mg sin theta)/m=g sin theta....(ii)`
and `a_(2)=(mg sin theta-mu mg cos theta)/m=g sin theta-mu g cos theta....(iii)`
from (i),(ii) and (iii)
we get `mu=0.75`