Question

the radius of the circular path of a particle is doubled but frequency of rotation is kept constant if the initial centripetal force be F then find the value of centripet force will be​

Answer 1

The new centripetal force becomes half of the initial value of force.

Explanation:

Let v is the velocity of the particle and r is the radius of circular path. The force exerted by the particle on the circular path is called centripetal force. Its expression is given by :

$F=\dfrac{mv^2}{r}$

According to given condition, if the radius of the circular path of a particle is doubled, r' = 2r

Let F' is new centripetal force. It is given by :

$F'=\dfrac{mv^2}{r'}$

$F'=\dfrac{mv^2}{(2r)}$

$F'=\dfrac{1}{2}\times \dfrac{mv^2}{(r)}$

$F'=\dfrac{1}{2}\times F$

So, the new centripetal force becomes half of the initial value of force.

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Topic : Centripetal force

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