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One end of massless inextensible string ...

One end of massless inextensible string of length `l` is fixed and other end is tied to a small ball of mass `m`. The ball is performing a circular motion in vertical plane. At the lowest position, speed of ball is `sqrt(20gl)`. Neglect any other forces on the ball except tension and gravitational force. Acceleration due to gravity is `g`.
During circular motion, minimum value of tension in the string`-`

A

zero only if `m_(1)=m_(2)`

B

`mg`

C

`10mg`

D

`15mg`

Text Solution

Verified by Experts

The correct Answer is:
D
Tension in the string is minimum when ball is at the highest position.By conservation of energy `(1)/(2)mv^(2)+mg (2l)=(1)/(2) m (20gl)`
`v^(2)=16gl` where `v` is the velocity of ball at the highest point.
So `T+ mg =(mv^(2))/(l)`
`T=(m16gl)/(l)-mg=15mg`
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