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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
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B
2m
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C
12m
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D
3.33m
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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 $$g \sin 45^o = 4g \cos 45^o$$
$$g\left(\dfrac{1}{5^2} \right) = (0.3 x) \dfrac{g}{5}$$
$$\dfrac{10}{3} m = x$$
$$x = 3.33 m$$

1432851_1011423_ans_05b25f96b7414afd9e3755c547a24d38.png

Physics

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