Question

Two bodies of masses 10 kg and 5 kg moving in concentric orbits of radii r and r such that their periods are the same . Then the ratio between their periods are the same . Then the ratio between their centripetal acceleration is

Answer 1

centripetal acclr = v²/r

& time period = 2π/ω

since time period is same then ω will also same

and  v = ωr

=> ca1/ca2 = v1²*r2/v2²*r1

on putting v1=ω1r1 & v2=.....

we get

r1 : r2    (answer)

Answer 2

Answer:

The ratio between their centripetal acceleration is r₁:r₂.

Explanation:

Given that,

Mass of first body = 10 kg

Mass of second body = 5 kg

Radius of first orbit = r

Radius of second orbit = r

The time periods are same then $\omega$ will be same

We need to calculate the centripetal acceleration

Using formula of centripetal acceleration

$a=\dfrac{v^2}{r}$....(I)

The value of velocity

$v = \omega r$

Now, The ratio between their centripetal acceleration

$\dfrac{a_{c_{1}}}{a_{c_{2}}}=\dfrac{v_{1}^{2}\times r_{2}}{v_{2}^2\times r_{1}}$

Put the value of v in equation (I)

$\dfrac{a_{c_{1}}}{a_{c_{2}}}=\dfrac{\omega^{2}\times r_{1}^2\times r_{2}}{\omega^2\times r_{2}^2\times r_{1}}$

$\dfrac{a_{c_{1}}}{a_{c_{2}}}=\dfrac{r_{1}}{r_{2}}$

Hence, The ratio between their centripetal acceleration is r₁:r₂.