Question

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 \(\mu=0.3x\), where \(x\) is distance travelled down the plane. The body will have maximum speed (for \(g=10\ \mathrm{m/s^2}\)) when \(x=\)

• A. 9.8 m
• B. 27 m
• C. 12 m
• D. 3.33 m

Hint:

Speed is maximum when the acceleration along the plane becomes zero: \(g\sin45^\circ=\mu g\cos45^\circ\).

Answer 1

The Correct Option is D

Acceleration down the plane: \(a=g\sin45^\circ-\mu g\cos45^\circ=\frac{g}{\sqrt2}(1-\mu)=\frac{g}{\sqrt2}(1-0.3x)\).
The body speeds up while \(a \gt 0\) and slows down once \(a \lt 0\), so the speed is maximum when \(a=0\).
\(1-0.3x=0\Rightarrow x=\frac{1}{0.3}=3.33\) m.
Answer: (4) 3.33 m