If the gravitational force between sun and earth is inversely proportional to r3 , where r is distance between earth and sun. Then which of the following statements are correct.

Book Online Demo

Check Your IQ

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

If the gravitational force between sun and earth is inversely proportional to $r^{3}$ , where r is distance between earth and sun. Then which of the following statements are correct.

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

Its orbit around sun can’t be a stable elliptical orbit.

Its orbit around sun can’t be a stable circular orbit.

Motion of earth around sun will be in one plane.

Tidal forces acting on earth will be inversely proportional to $r^{4}$ .

answer is A, B, C, D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

1. Motion is in one plane by conservation of angular momentum
2. $m ω^{2} r = \frac{m v^{2}}{r} = \frac{{(m v r)}^{2}}{m r^{3}} = \frac{L^{2}}{m r^{3}}$
Question Image
Let equilibrium radius be $∴ (\frac{L^{2}}{m r_{0}^{3}} + \frac{K}{r_{0}^{3}})$ or $K = \frac{L^{2}}{m}$
In general force on earth
$F = (\frac{L^{2}}{m r^{3}} - \frac{K}{r^{3}}) \frac{d F}{d r} = (\frac{- 3 L^{2}}{m r^{4}} + \frac{3 K}{r^{4}})$
$\frac{d F}{d r} = 3 (K - \frac{L^{2}}{m}) [\frac{1}{r^{4}}) = 0$
This represents neutral equilibrium
3. Tidal forces are proportional to $\frac{d F}{d r}$