Question

A block of mass $4kg$ 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 $14.14N$. Find $\theta$ ?

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

Answer 1

Answer: (B)

Given, $m=4kg,{\mu }_s=0.5$
$f{r}_k=14.14N=10\sqrt{2}N$
Normal reaction force,
$N=mg\cos \theta =4\times 10\times \cos \theta =40\cos \theta$
and kinetic friction,
$\Rightarrow f{r}_k={\mu }_{s}N$
$\Rightarrow 10\sqrt{2}=0.5\times 40\cos \theta$
$\Rightarrow 10\sqrt{2}=\frac{1}{2}\times 40\cos \theta$
$\Rightarrow 10\sqrt{2}=20\cos \theta$
$\Rightarrow \cos \theta =\frac{10\sqrt{2}}{20}$
$\Rightarrow \cos \theta =\frac{1}{\sqrt{2}}$
$\Rightarrow \theta =45^{\circ }$