Coefficient Of Friction Between A Body And Wedge - Practice Questions & MCQ

• If the same wedge is made rough then the time taken by it to come down becomes n  times more (nt) 

Then find the Coefficient of Friction between body and wedge in term of n?

For this make 2 cases

Case 1- A body slides on a smooth wedge of angle θ and its time of descent is t.

Case 2- If the same wedge made rough then the time taken by it to come down becomes n times more (i.e., nt)

(The length of the path in both cases are the same)

For smooth wedge

$$\begin{array}{rl}& S=u\cdot t+\frac{1}{2}a{t}^2\\ & S=\frac{1}{2}(g\sin \theta )t^2\\ & \mathrm{u}=0\\ & a=g\sin \theta \end{array}$$

For Rough wedge

$$S=\frac{1}{2}g[\sin \theta -\mu \cos \theta ](nt{)}^2$$

(i) $=$ (ii)

$$\mu =\tan \theta [1-\frac{1}{n^2}]$$

$\mu =\text{coefficient of friction }$
$\theta =$ Angle of inclination
$\mathrm{n}=$ an integer