First slide

making equation on system

Question

A bead of mass m is released from rest at A to move along the fixed smooth circular track as shown in Fig. The ratio of magnitudes of centripetal force and normal reaction by the track on the bead at any point $P_{0}$ described by the angle $θ$ ( $\neq 0$ ) would

Easy

A

Increase with $θ$
B

Decrease with $θ$
C

Remain constant
D

First increase with $θ$ and then decrease

Solution

Conservation of energy gives
$\frac{1}{2} m v^{2} = m g R \sin θ$
$\frac{m v^{2}}{R}$ =2mg sin $θ$ = $F_{C}$ $\Rightarrow$ Now, N – mg sin $θ$ = $F_{C}$
N = 3 mg sin $θ$ $\Rightarrow$ $\frac{F_{C}}{N} = \frac{2}{3}$

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