Question

A ball of mass (m) 0.5 kg is attached to
the end of a string having length (l)
0.5 m. The ball is rotated on a horizontal
circular path about vertical axis. The
maximum tension that the string can bear
is 324 N. The maximum possible value
of angular velocity of ball (in rad/s) is

• A. 9
• B. 18
• C. 27
• D. 36

Answer 1

Answer: (D)

$r=lsin\theta$
$Tcos\theta$ component will cancel mg.
$Tsin\theta$ component will provide necessary centripetal force
to the ball towards centre C.
$\therefore Tsin\theta =mr{\omega }^2=m(lsin\theta ){\omega }^{2}orT=ml{\omega }^2$
$\therefore \omega =\sqrt{\frac{T}{ml}}$
or ${\omega }_{max}=\sqrt{\frac{T_{max}}{ml}}=\sqrt{\frac{324}{0.5\times 0.5}}$
$=36rad/s$
$\therefore$ Correct option is (d).