Question

A stone tied to a string is rotated in a vertical circle. The minimum speed with which the stone has to be rotated in order to complete the circle :

A

decreases with increasing the mass of the stone

B

is independent of the mass of the stone

C

decreases with increasing the length of the string

D

is independent of the length of the string

Easy
Solution
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Correct option is B)


Let be the minimum speed required at .
Apply energy conservation between point and we get
             
Taking point as zero potential level
                 

From equation , we observe that mass is cancelled on both sides.
is independent of .


At highest point, Tension will be zero for minimum velocity
gravitational pull will provide necessary centripetal force

           

            .... Putting in equation

We get,

           

is proportional to the square root of .
Hence option is correct.

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