Question

A block rests on a rough incline 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. $2.5$
• B. $4.0$
• C. $1.6$
• D. $2.0$

Answer 1

The correct option is D $2.0$

We know that static frictional force $f_s={\mu }_{s}N$
$f_s={\mu }_{s}mg\cos \theta$
$f_s=0.8\times m\times \frac{10\times \sqrt{3}}{2}$
$=4\sqrt{3}m$
As friction balances block's mass component along the incline
$f_s>mg\sin {30}^{\circ }$
$\therefore f=mg\sin {30}^{\circ }=10\text{N}$
$\Rightarrow \frac{m\times 10}{2}=10$
$\Rightarrow m=2\text{kg}$