question_answer

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

Correct Answer: D

Solution :

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