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A ball of mass 0.1kg is suspended by a s...

A ball of mass `0.1kg` is suspended by a string `30 cm` long Keeping the string always taut the ball describe a horizontal circle of radius `15cm` Calculate the angular speed of the ball .

Text Solution

Verified by Experts

The correct Answer is:
`6.14`
The situation is shown in

Here `m=0.1kg`, `r=15cm=0.15m`
Let the string make angle `theta` with the vertical . Then
`sintheta=(AB)/(OA)=(15)/(30)=(1)/(2)` or `theta=30^(@)`
Let T be the tension in the string. Its vertical component balances the weight mg while the horizontal component `T sin theta` provides the centripetal force.
`:. T cos theta=mg`..........(i)
And `T sin theta=mr omega^(2)`.........(ii)
Dividing (ii) by (i) , we get
`(T sin theta)/(T cos theta)=(mromega^(2))/(mg)` or `tan theta=(romega^(2))/(g)`
or `omega=sqrt((g tan theta)/(r))=sqrt((9.8xxtan30^(@))/(0.15))`
`=6.14rads^(-1)`
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