Question

Starting from rest, a body slides down a ${45}^o$ 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

• A. 0.33
• B. 0.25
• C. 0.75
• D. 0.8

Answer 1

The correct option is C 0.75

Without friction
on 45 inclination acceleration due to gravity along the surface (a) = $gsin45$ $=$ $\frac{g}{\sqrt{2}}$
applying $S=ut+\frac{1}{2}a{t}^2$
where $S$ is distance along surface in time t.
According to question, initial velocity u = 0
$\therefore$ $S=\frac{1}{2}a{t}^2$
S $=$ $\frac{g{t}^2}{2\sqrt{2}}$ ----- (1)
With friction
acceleration due to gravity = $gsin45-\mu gcos45$ $=$ $\frac{g}{\sqrt{2}}(1-\mu )$
with friction same S distance travel in 2t time.
again applying $S=\frac{1}{2}a{t}^2$ as initial velocity (u) = 0
S $=$ $\frac{g(1-\mu ){\left(2t\right)}^2}{2\sqrt{2}}$ ------(2)
Equating right side of equations (1) and (2)
$\frac{g{t}^2}{2\sqrt{2}}$ = $\frac{g(1-\mu ){\left(2t\right)}^2}{2\sqrt{2}}$
or $(1-\mu )=\frac{1}{4}$
or $\mu =\frac{3}{4}=0.75$
So, C is correct answer.