Question

A string can take maximum tension of 10 kg wt. If the string is used to revolve a body of mass 1.2 kg in a horizontal circle of radius 50 cm, what is the maximum speed with which the body can be revolved ? When revolving at maximum speed, what are the period and frequency of revolutions of the body ?

Answer 1

Maximum Tension, $T_{max}=10\times g$

$⟹T_{max}=100$ $N$

$\therefore \frac{m{V}^2}{r}\le 100$

$⟹V_{max}^2=\frac{100\times r}{m}$

$⟹V_{max}=\sqrt{\frac{100\times 50\times {10}^{-2}}{1.2}}$

$⟹V_{max}=6.45$ $m/s$

And, $V_{max}=\frac{2\pi r}{T}$

Time period, $T=\frac{2\pi r}{V_{max}}$

$⟹T=\frac{2\pi \times 50\times {10}^{-2}}{6.45}$

$⟹T=0.487$ $s$

Frequency, $\omega =\frac{2\pi }{T}=12.90$ $rad/s$