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

Solution

## 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 $$g \sin 45^o = 4g \cos 45^o$$$$g\left(\dfrac{1}{5^2} \right) = (0.3 x) \dfrac{g}{5}$$$$\dfrac{10}{3} m = x$$$$x = 3.33 m$$Physics

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