Question

A body is moving down an inclined plane of slope ${37}^{\circ }$. The coefficient of friction between the body and the plane varies as $\mu =0.3x$, where $x$ is the distance travelled down the plane by the body. The value of $x$ for which the body will have maximum speed is $(\sin {37}^{\circ }=\frac{3}{5})$

• A. $2.5m$
• B. $5m$
• C. $7.5m$
• D. $10m$

Answer 1

The correct option is A $2.5m$

When the body has maximum speed, the acceleration is zero.
Hence,
$mg\sin \theta =\mu mg\cos \theta$
$\tan \theta =\mu$
$\tan {37}^{\circ }=0.3x$

$\frac{3}{4}=0.3x\Rightarrow x=2.5m$