Question

A block starts moving up an inclined plane of inclination $30^{\circ}$ with an initial velocity of $v_{0}$. It comes back to its initial position with velocity $\frac{v_{0}}{2} .$ The value of the coefficient of kinetic friction between the block and the inclined plane is close to $\frac{I }{1000}$, The nearest integer to $I$ is _______.

Answer 1

$\therefore \frac{1}{2} v _{0} \frac{ v _{0}}{ a _{1}}=\frac{1}{2}\left(\frac{ v _{0}}{2}\right)\left(\frac{ v _{0}}{2 a _{1}}\right)$
$\Rightarrow \,3 \,\sin \,\theta=5 \,\mu\, \cos\, \theta$
$\therefore \mu=\sqrt{3} / 5$