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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 $30^\circ$, the box starts to slip and slides 4.0 m down the plank in 4.0 s. 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
Detailed Solution
$\mu_s = \tan 30^\circ = \frac{1}{\sqrt3} \approx 0.6$
$a = g\sin30^\circ - \mu_kg\cos30^\circ$
$s = ut + \frac{1}{2}at^2$: $4 = \frac{1}{2}\left[\frac{g}{2} - \mu_k\frac{\sqrt3 g}{2}\right]\times 16$
$\mu_k \approx 0.5$
$a = g\sin30^\circ - \mu_kg\cos30^\circ$
$s = ut + \frac{1}{2}at^2$: $4 = \frac{1}{2}\left[\frac{g}{2} - \mu_k\frac{\sqrt3 g}{2}\right]\times 16$
$\mu_k \approx 0.5$