Question

A body is in uniform circular motion with centripetal acceleration a. If its speed get tripled, then the ratio of centripetal acceleration after and before the change is

Answer 1

Given:

A body is in uniform circular motion with centripetal acceleration a. Its speed get tripled.

To find:

Ratio of centripetal acceleration after and before the change.

Calculation:

General expression for centripetal acceleration with Velocity u and radius R is:

$\boxed{\rm{\blue{acc. = \dfrac{{u}^{2}}{R}}}}$

Let initial velocity be v ;

So, before the change:

$\therefore \: \sf{a1 = \dfrac{ {v}^{2} }{r} }$

$= > \: \sf{a = \dfrac{ {v}^{2} }{r} =a1}$

Final velocity be 3v ;

So, after the change:

$\therefore \: \sf{a2 = \dfrac{ {(3v)}^{2} }{r} }$

$= > \: \sf{a2 = \dfrac{9 {v}^{2} }{r} }$

$= > \: \sf{a2 = 9a }$

Hence , required ratio :

$\boxed{ \red{ \bold{ \large{a2 : a1 = 9 : 1}}}}$

Answer 2

The ratio of centripetal acceleration after and before the change is 9 : 1

Explanation:

If the velocity of the body is v

Then the centripetal acceleration of the body is given by

$a=\frac{v^2}{R}$

Where R is the radius of the circular path

Therefore, if the velocity is tripled then new velocity = 3v

New centripetal acceleration

$a'=\frac{(3v)^2}{R}$

$\implies a'=\frac{9v^2}{R}$

The ratio of centripetal acceleration after and before the change

$=\frac{a'}{a}$

$=\frac{9v^2/R}{v^2/R}$

$=9:1$

Hope this answer is helpful.

Know More:

Q: When a body is moving in circular path with acceleration a if its velocity gets doubled find the ratio of acceleration after n before the change?

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