Question

A body starts from rest on a long inclined plane of slope ${45}^o$. The coefficient of friction between the body and the plane varies as $\mu =0.3x$, where $x$ is the distance travelled down the plane. The body will have maximum speed (for $g=10m/s^2$) when $x=$:

• A. $9.8m$
• B. $2m$
• C. $12m$
• D. $3.33m$

Answer 1

The correct option is D $3.33m$

$N=mg\cos {45}^o$

acceleration = $g\sin 45$

deceleration = $\mu g\cos {45}^o$

Net acceleration = $(g\sin {45}^o-4g\cos {45}^o)$

max speed will be reached

when $g\sin {45}^o=4g\cos {45}^o$

$g\left(\frac{1}{5^2}\right)=\left(0.3x\right)\frac{g}{5}$

$\frac{10}{3}m=x$

$x=3.33m$