Question

A particle of mass $1$ kg is revolved along the horizontal circle of a radius $1$ m with the help of a string. If the maximum tension the string can withstand is 16${\pi }^2$ N, then the maximum frequency with which the particle can revolve is:

• A. $3$ rps
• B. $2$ rps
• C. $4$ rps
• D. $5$ rps

Answer 1

The correct option is B $2$ rps

A mass $m=1kg$ is revolved around a horizontal circle (thus no effect of graffiti )

along a radius of $r=1m$.

The man experiences a centripetal force :

$F_e=mr{w}^2$ [$w$ : Angular frequency ]

This centripetal force is provided by the tension is string.

$\Rightarrow T=F_e=mr{w}^2$

as given $T=16{\pi }^{2}N$, we get :

$16{\pi }^2=\left(1\right)\left(1\right)w^2$

$\Rightarrow w^2=16{\pi }^2\Rightarrow w=4\pi$

Thus, frequency of rotation.

$v=\frac{w}{2\pi }=2.$