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

Options

A. `9`
B. `18`
C. `27`
D. `36`

Answer

d

Explanation

As shown in
`R = AO = L sin theta`
Resolving tension `T` of string at `A` into two rectangular components `T sin theta` acts along `AO` and `Tcos theta` acts vertically upwards As ball describes a horizontal circular path of radius `R` so the horizontal component of tension `(=T sin theta)` provides the required centripeta force
`T sin theta = omega^(2) R = m omega^(2) L sin theta`
or `T = m omega^(2) L`
or `omega = sqrt((T)/(mL)) = sqrt((324)/(0.5 xx 0.5)) = 36 rad//s`
.