A block slides from an inclined plane of inclination `45^(@)`If it takes twice the time with friction than that without friction, the coefficient of friction between block and surface is :

Options

A. 1
B. `0.75`
C. `0.5`
D. `0.25`

Answer

b

Explanation

Acc. without friction `a_(1) = g sin theta`
Acc. with friction `a_(2) = g sin theta- mug cos theta`
Now `(t_(1))/(t_(2))=sqrt(a_(2)/(a_(1))) or(t_(2))/(t_(1))=sqrt(a_(1)/(a_(2)))`
`2=sqrt((gsintheta)/(gsin theta- mug cos theta))`
`4=(sin theta)/(sin theta-mu cos theta)=(1)/(1-mu tan theta)`
`4=(1)/(1-mu)=1 or(As theta=45^(@)`
`4-4mu=1 or 4mu=3mu=3//4=0.75`
(b) is the choice.