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. $1.6\text{kg}$
• D. $2\text{kg}$

Answer 1

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

The force applied will be component of weight along the incline $=mg\sin \theta =m\left(10\right)\sin {30}^{\circ }=5m\text{N}$

For block to be in rest friction should balance applied force $f=mg\sin 30$
$\therefore f=mg\sin 30=10\text{N}$
$\Rightarrow \frac{m\times 10}{2}=10$
$\Rightarrow m=2\text{kg}$