Question

A car is moving in a circular horizontal track of radius $\frac{6 \sqrt{3}}{5}\text{m}$ A plumb bob is suspended from the roof of the car by a light rigid rod. The angle made by the rod with the vertical is $60^{o}.$ Then the car moves with a constant speed of _______ $\mathrm{m} / \mathrm{s} \cdot\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)$

Answer 1

$\text{T}sin \theta =\frac{\text{mv}^{2}}{\text{R}}$
$\text{T}cos \theta =\text{mg}$
$\therefore \, tan \theta =\frac{\text{v}^{2}}{\text{Rg}}$
$\therefore \, v^{2}=tan \theta \times R\times g$
$\therefore \, v^{2}=tan 60^{o}\times \frac{6 \sqrt{3}}{5}\times 10$
$\therefore \, v^{2}=\sqrt{3}\times \frac{6 \sqrt{3}}{5}\times 10$
$\therefore \, v^{2}=36$
$\therefore \, v=6 \, \text{m}/\text{s}$