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

Answer: 6

$\text{T}sin\theta =\frac{{\text{mv}}^2}{\text{R}}$
$\text{T}cos\theta =\text{mg}$
$\therefore tan\theta =\frac{{\text{v}}^2}{\text{Rg}}$
$\therefore v^2=tan\theta \times R\times g$
$\therefore v^2=tan60^o\times \frac{6\sqrt{3}}{5}\times 10$
$\therefore v^2=\sqrt{3}\times \frac{6\sqrt{3}}{5}\times 10$
$\therefore v^2=36$
$\therefore v=6\text{m}/\text{s}$