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Friction and Horizontal Circular Motion Problems

A small mass ...

Question

A small mass $m$ starts sliding down a smooth and stationary semi circular track. Which of the following graph best represents the variation of magnitude of the force applied by the track on the mass and the angle $θ$ ( assume initially $θ = 0$ ?

A

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B

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C

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D

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Solution

The correct option is B

By energy conservation, we have
$\frac{1}{2} m v^{2} = m g R s i n θ From Newtons laws of motion and Free Body Diagram \Rightarrow \frac{m v^{2}}{R} = N - m g s i n θ N = \frac{m v^{2}}{R} + m g s i n θ N = 3 m g s i n θ$

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