Question

A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches ${30}^0$, the box starts to slip and slides $4m$ down the plank in $4s$. The coefficients of static and kinetic friction between the box and the plank will be, respectively

• A. $0.4$ and $0.3$
• B. $0.6$ and $0.6$
• C. $0.6$ and $0.5$
• D. $0.5$ and $0.6$

Answer 1

The correct option is C $0.6$ and $0.5$

Coefficient of static friction is ${\mu }_s=\tan {30}^0=0.577\approx 0.6$
For coefficient of kinetic friction, $ma=mg\sin {30}^0-f$
$=mg\sin {30}^0-{\mu }_{k}mg\cos {30}^0....\left(1\right)$
and also using $S=ut+\frac{1}{2}a{t}^2\Rightarrow 4=0+\frac{1}{2}a(4{)}^2$
or $a=0.5m/s^2$
Now from (1) we get, $0.5=10\times \frac{1}{2}-{\mu }_k\left(10\right)\left(\frac{\sqrt{3}}{2}\right)$
or ${\mu }_k=\frac{4.5}{5\sqrt{3}}=0.5$