Question

A stone of mass m is tied to a string and is moved in a vertical circle of radius r making n revolution per minute. The total tension in the string when the stone is at its lowest point is

• A. $mg$
• B. $m(g+\pi n{r}^2)$
• C. $m(g+nr)$
• D. $m(g+\frac{{\pi }^2{n}^{2}r}{900})$

Answer 1

Answer: (D)

$m(g+\frac{{\pi }^2{n}^{2}r}{900})$

Tension in string when it reach lower-most point

$T=mg+m{\omega }^{2}r$

$=m(g+4{\pi }^2{n}^{2}r)$ [as $\omega =2\pi n$]

$=m(g+4{\pi }^2{\left(\frac{n}{60}\right)}^{2}r)$

$=m(g+\left(\frac{{\pi }^2{n}^{2}r}{900}\right))$