Question

A block of mass $2\text{kg}$ slides down an incline plane of inclination ${30}^{\circ }$. The coefficient of friction between block and plane is $0.5$. The contact force between block and incline plane is :

• A. $25N$
• B. $10\sqrt{3}N$
• C. $5\sqrt{7}N$
• D. $5\sqrt{15}N$

Answer 1

The correct option is D $5\sqrt{15}N$


Now FBD for the block

$N=mg\cos \theta =2\times 10\times \frac{\sqrt{3}}{2}$
$N=10\sqrt{3}$
$f=\mu N$
$=0.5\times 10\sqrt{3}$
$=5\sqrt{3}$
$F_{net}=\sqrt{N^2+f^2}$
$=\sqrt{300+75}$
$=\sqrt{375}$
$=\sqrt{15\times 25}$
$=5\sqrt{15}N$