Question

A block of mass $m$ is placed over rough inclined plane having inclination $30^\circ $ . The co-efficient of friction between the block and the inclined plane is $0.75$ . The contact force on the block is

• A. $\frac{3}{4}mg$
• B. $2mg$
• C. $\frac{5}{4}mg$
• D. $mg$

Answer 1

Answer: (D)

$mgsin \theta =\frac{\sqrt{3}}{2} \, mg=f$
$f_{l}=μmgcos \theta $
$=\frac{3}{4}mg\frac{\sqrt{3}}{2}=\frac{3 \sqrt{3}}{8}mg$
$f < f_{r} \, $
$f=mgsin \theta $
$N=mgcos \theta $
$f_{net}=mg\sqrt{sin^{2} \theta + cos^{2} ⁡ \theta }$
$=mg$