Question

A mass of 2 kg is hung by a string of length 1.5 m as shown in the figure. The mass revolves in a horizontal circular path at 50 revolutions per minute.


The tension in the string in Newtons is

• A. $25\pi /3$
• B. $25{\pi }^2/3$
• C. $50\pi /3$
• D. $50{\pi }^2/3$

Answer 1

The correct option is B $25{\pi }^2/3$



$Tcos\theta =mg$

$Tsin\theta =mr{\omega }^2$

$tan\theta =\frac{r{\omega }^2}{g}$

$r=lsin\theta$

$\frac{sin\theta }{cos\theta }=\frac{lsin\theta {\omega }^2}{g}$

$cos\theta =\frac{g}{l{\omega }^2}$

$T=\frac{mgl{\omega }^2}{g}=ml{\omega }^2=2\times 1.5{\left(\frac{2\pi 50}{60}\right)}^2=25\frac{{\pi }^2}{3}$