Question

A ball of mass $0.12\, kg$ is being whirled in a horizontal circle at the end of string $0.5\, m$ long. It incapable of making $231$ revolutions in one minute. The breaking tension of the string is

• A. 3N
• B. 15.1 N
• C. 31.5 N
• D. 35.1 N

Answer 1

Answer: (D)

When body performs circular motion, it is acted upon by a centripetal force the magnitude of which is given by $F=\frac{m v^{2}}{r}$
where, $m$ is mass, $v$ the velocity and $r$ the radius.

Since, $ v=r \omega $
$ \therefore F=m r \omega^{2} $
Given, $ m=0.12 \,kg , r=0.5\, m , $
$ \omega=231\, rpm =\frac{2 \pi \times 231}{60} rad / s =24.2\, rad / s $
$ \therefore F=0.12 \times 0.5 \times(24.2)^{2}=35.1\, N $