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 traveled down the plane by the body. The body will have maximum speed. $(\sin {37}^{\circ }=\frac{3}{5})$

• A. at x=1.16m
• B. at x=2m
• C. at bottommost point of the plane
• D. at x=2.5m

Answer 1

Answer: (D)

at x=2.5m

velocity will be maximum when $\frac{dv}{dt}=0$. i.e $a=0$

$gsin\theta =\mu gcos\theta$

$tan\theta =\mu =0.3x=0.75$

$x=2.5$ m