Question

the speed of a body moving in uniform circular motion is double and the radius of circular path is halved what happens to centripetal force ​

Answer 1

Centripetal acceleration is given by a = v²/R

 Hence, if v is doubled and R is halved, we get a = 4v²/(R/2) = 8a

∴ If uniform circular motion is doubled and the radius of the circular path is halved then, the Centripetal Force will be 8 times.

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Answer 2

Given:

• Speed of body is doubled, and radis halved.

To find:

New Centripetal Force ?

Calculation:

• Let initial Centripetal Force be F = mv²/r.

Now,

• new speed = 2v
• new radius = r/2.

So, new Centripetal Force:

$\sf F_{2} = \dfrac{m {(2v)}^{2} }{ (\dfrac{r}{2} )}$

$\sf \implies F_{2} = 8 \times \dfrac{m {v}^{2} }{r}$

$\sf \implies F_{2} = 8 \times F$

So, new force becomes 8 times the initial force.