Question

The time taken by a body to slide down a rough ${45}^o$ incline plane is twice that required to slide down a smooth ${45}^o$ incline plane The coefficient of kinetic friction between the object and rough plane is given by:

• A. $\frac{1}{3}$
• B. $\frac{3}{4}$
• C. $\sqrt{\frac{3}{4}}$
• D. $\sqrt{\frac{4}{3}}$

Answer 1

The correct option is B $\frac{3}{4}$

Acceleration along the downward directioon of wedge

${\alpha }_1\frac{(mgsin{45}^{\circ }-\mu mgcos{45}^{\circ })}{m}$

$=\frac{(1-\mu )g}{\sqrt{2}}$

Let total time taken is $t,S=o\times t+0.5\left(\mu \right)t^2$

when wedge is friction less

then acceleration

$a_2=\frac{g}{\sqrt{2}}$

$8=o\times \frac{t}{2}+.5\left(a_2\right)\times (\frac{t}{2}{)}^2$

Equate both value of S

$\mu =\frac{3}{4}$

Hence (B) is correct answer