Question

A block rests on a rough inclined plane making an angle of ${30}^{\circ }$ with the horizontal. The coefficient of static friction between the block and the plane is $0.8$. If the frictional force on the block is $10\text{N}$, the mass of the block (in $\text{kg}$) is (take $g=10{\text{m/s}}^2$)

• A. $2.5\text{kg}$
• B. $4\text{kg}$
• C. $1.5\text{kg}$
• D. $2\text{kg}$

Answer 1

The correct option is D $2\text{kg}$

By the FBD, It is given that the body is in rest and so the frictional force $10\text{N}$ will be acting on the block opposite to the direction of component of $mg$ along the incline plane.
$\therefore f=mg\sin 30=10\text{N}$
$\Rightarrow \frac{m\times 10}{2}=10$
$\Rightarrow m=2\text{kg}$