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A ball of mass (m) 0.5 kg is attached to...

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 radian//s) is -
.

A

`9`

B

18

C

27

D

36

Text Solution

Verified by Experts

The correct Answer is:
D
The tension is resolved into horizontal copmponent T ` sin theta ` and vertical component `T cos theta `. ` T sin theta ` provides the centripetal force required for the horizontal circular motion

`therefore T sin theta = (mv^(2))/(r ) = m r omega ^(2)`
From the figure ` sin theta = (BC)/(OB) =(r )/(L )`
` therefore T. (r )/(L ) = m r omega ^(2) therefore T= Lomega ^(2)`
` omega^(2) = (T )/(mL ) = (324 )/((1)/(2)xx(1)/(2) )=324 xx4`
` therefore omega = sqrt(324xx4)=18 xx2=36 rad //s`
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