Question

A block of mass $1kg$ is kept on a rough inclined plane of angle ${30}^{\text{o}}$. Find the frictional force acting on the block. Given coefficient of friction $\mu =0.8$

• A. $4.9\text{N}$
• B. $6.7\text{N}$
• C. $10\text{N}$
• D. Zero

Answer 1

The correct option is A $4.9\text{N}$

As the block is kept on the inclined plane, the normal will be $mg\cos \theta$ and the force on the block along the plane will be $mg\sin \theta$.

We also know that Maximum Frictional force $f_L=\mu N=\mu mg\cos {30}^{\circ }=0.8\times 9.8\times \frac{\sqrt{3}}{2}=6.7\text{N}$
while applied force $=mg\sin {30}^{\circ }=1\times 9.8\times \frac{1}{2}=4.9\text{N}<f_L$
$($If $g$ is not given, we consider it as $9.8{\text{m/s}}^2)$

Hence, frictional force will be equal to applied force.
$f=4.9\text{N}$