Question

A string breaks under tension of 10kg weight.if string is use to involved a body of mass 1.2kg in horizontal circle of radius 50cm .what is maximum speed with which the body can be revolved?what is its period?

Answer 1

Let $\displaystyle\sf {g=10\ m\ s^{-2}.}$

In the case of horizontal circular motion, the tension in the string balances the necessary centripetal force acting on the 1.2 kg mass, i.e.,

$\displaystyle\longrightarrow\sf {T=\dfrac {mv^2}{r}}$

$\displaystyle\longrightarrow\sf {v=\sqrt{\dfrac {Tr}{m}}}$

Given,

• $\displaystyle\sf {T=100\ N}$

(This is the maximum possible value since the string breaks under 10 kgwt = 100 N)

• $\displaystyle\sf {r=50\ cm=0.5\ m}$

• $\displaystyle\sf {m=1.2\ kg}$

Then, velocity,

$\displaystyle\longrightarrow\sf {v=\sqrt{\dfrac {100\times0.5}{1.2}}}$

$\displaystyle\longrightarrow\sf {v=\sqrt{\dfrac {125}{3}}}$

$\displaystyle\longrightarrow\sf {\underline {\underline {v=6.46\ m\ s^{-1}}}}$

And time period,

$\displaystyle\longrightarrow\sf {t=\dfrac {2\pi r}{v}}$

$\displaystyle\longrightarrow\sf {t=\dfrac {2\times 3.14\times 0.5}{6.46}}$

$\displaystyle\longrightarrow\sf {\underline {\underline {t=0.49\ s}}}$