First slide

Vertical circular motion

Question

A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/s. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle made by the rod with the track is

Moderate

A

zero
B

$30^{\circ}$
C

$45^{\circ}$
D

$60^{\circ}$

Solution

The different forces acting on the bob are shown in
From figure we have
$\begin{array}{l} mgsin θ = \frac{{mv}^{2}}{R} \cos θ \\ ∴ \tan θ = \frac{v^{2}}{gR} = \frac{(10)^{2}}{10 \times 10} = 1 \\ θ = \tan^{- 1} (1) = 45^{\circ} \end{array}$

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