Question

A block of mass $4 \,kg$ rest on a rough inclined plane making an angle of $\theta$ with the horizontal. The coefficient of static friction between the block and plane is $0.5$ and the frictional force on the block is $14.14 \,N$. Find $\theta$ ?

• A. $30^{\circ}$
• B. $45^{\circ}$
• C. $60^{\circ}$
• D. $15^{\circ}$

Answer 1

Answer: (B)

Given, $m=4 kg , \mu_{s}=0.5$
$f r_{k}=14.14 N=10 \sqrt{2} N$
Normal reaction force,
$N=m g \cos \theta=4 \times 10 \times \cos \theta=40 \cos \theta$
and kinetic friction,
$\Rightarrow f r_{k}=\mu_{s} N$
$ \Rightarrow 10 \sqrt{2}=0.5 \times 40 \cos \theta $
$\Rightarrow 10 \sqrt{2}=\frac{1}{2} \times 40 \cos \theta$
$\Rightarrow 10 \sqrt{2}=20 \cos \theta $
$\Rightarrow \cos \theta=\frac{10 \sqrt{2}}{20}$
$\Rightarrow \cos \theta=\frac{1}{\sqrt{2}}$
$ \Rightarrow \theta=45^{\circ}$