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

is independent of the mass of the stone
is independent of the length of the string
decreases with increasing mass of the stone
decreases with increasing length of the string

Correct answer: decreases with increasing length of the string

Solution

The minimum speed required to rotate a stone in a vertical circle is given by v = √(gL), where g is the acceleration due to gravity and L is the length of the string. This shows that the minimum speed decreases as the length of the string increases.

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