Question

A box of mass $m$ initially at rest on a plane inclined at an angle of $\theta$. Find out the maximum value for the coefficient of static friction at which the box will slide down the incline?

• A. $\sin \theta -\cos \theta$
• B. $\cos \theta -\sin \theta$
• C. $mg\sin \theta$
• D. $\frac{\sin \theta }{\cos \theta }$
• E. $\sin \theta +\cos \theta$

Answer 1

Answer: (D)

$\frac{\sin \theta }{\cos \theta }$

Let the maximum value of coefficient of static friction be $\mu$.

Thus maximum static frictional force $f_{max}=\mu N=\mu \left(mgcos\theta \right)$

For the box just to slide, $mgsin\theta =f_{max}$

$\therefore$ $mg$ $sin\theta =\mu mg$ $cos\theta$ $⟹\mu =\frac{sin\theta }{cos\theta }$