A body takes twice the time to slides down a rough inclined plane at 45° to an identical smooth inclined plane. What is the coefficient of friction of rough plane?

Options

A. 0.75
B. 0.5
C. 0.25
D. 0.15

Answer

A

Explanation

The acceleration of body sliding down a smooth and rough inclined planes respectively are,
`a_(1)=gsin45^(@)=g/(sqrt2)`
and `a_(2)=g(sin45^(@)-mu_(g)sin45^(@))`
`=g/(sqrt2)(1-mu_(k))`
where `mu_(k)` = coefficient of kinetic friction. Now as the square of the time of slide is inversely proportional to acceleration.
Therefore, `(t_(2)^(2))/(t_(1)^(2))=(a_(1))/(a_(2))=1/(1-mu_(k))`
Also, `t_(2)-2t_(1)`
`therefore4=1/(1-mu_(k))rArrmu_(k).=0.75`