Question

A coin of mass $10g$ is placed over a book of length $50cm$. The coin is on the verge of sliding when one end of the book is lifted $10cm$ up. The coefficient of static friction between the book and the coin is

• A. $1.0$
• B. $0.4$
• C. $0.3$
• D. $0.2$

Answer 1

The correct option is D

$0.2$

Step 1: Given data.

Mass of coin $=10g$

Length of book$=50cm$

Height$=10cm$

Upward force acting on the coin $=R$

Step 2: Find the coefficient of static friction.

Formula used:

$\sin \left(\theta \right)=\frac{\mathrm{Perpendicular}}{\mathrm{hypotaneous}}=\frac{10}{50}$ ... $\left(i\right)$

Now,

Using balance equation:

$mg\sin \left(\theta \right)=\mu R$

$\Rightarrow$$mg\sin \left(\theta \right)=\mu mg\cos \left(\theta \right)$ $\left[\because R=mg\cos \left(\theta \right)\right]$

$\Rightarrow$ $\tan \left(\theta \right)=\mu$ ...$\left(ii\right)$

$\Rightarrow$ $\begin{array}{rcl}\tan \left(\theta \right)& =& \frac{10}{\sqrt{{50}^2-{10}^2}}\\ & =& 0.2\end{array}$

$\Rightarrow$ $\mu =0.2$

Hence, The coefficient of static friction is $0.2$