A body starts from rest on a long inclined plane of slope $45^{\circ}$. The coefficient of friction between…
A body starts from rest on a long inclined plane of slope $45^{\circ}$. The coefficient of friction between the body and the plane varies as $\mu=0.3 x$, where $x$ is distance travelled down the plane. The body will have maximum speed (for $g=10 \mathrm{~m} / \mathrm{s}^2$ ) when $x=$
$9.8 \mathrm{~m}$
$27 \mathrm{~m}$
$12 \mathrm{~m}$
$3.33 \mathrm{~m}$
Solution
When the body has maximum speed then
$
\begin{aligned}
& \mu=0.3 \mathrm{x}=\tan 45^{\circ} \\
& \therefore \mathrm{x}=3.33 \mathrm{~m}
\end{aligned}
$