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Question

A block weighing $$10\ N$$ travels down a smooth curved track $$AB$$ joined to a rough horizontal surface (figure).The rough surface has a friction coefficient of $$0.20$$ with the block. If the block starts slipping on the track from a point $$1.0\ m$$ above the horizontal surface, the distance it will move on the rough surface is :
293258_6590ac4b8c704ea4b9bed25496f3adc1.jpg


A
5.0 m
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B
10.0 m
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C
15.0 m
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D
20.0 m
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Solution

The correct option is D $$5.0 \ m$$
Let the velocity at point B be $$V$$.
By conservation of energy, $$mgh=\dfrac{1}{2}mv^2\Rightarrow v=\sqrt{2gh}$$.
Now deceleration due to friction is $$a=\mu g=0.2g$$.
So stopping distance, $$s=\dfrac{v^2}{2a}=2gh/0.4g=5h=5\times1=5m$$

Physics

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