Question

If the law of gravitation , instead of being inverse-square law, becomes an inverse cube law :

• A. Planets will not have elliptic orbits
• B. Circular orbits of planets is not possible
• C. Projectile motion of some thrown by hand on the surface of the earth will be approximately parabolic
• D. there will be no gravitational force inside a spherical shell of uniform density.

Answer 1

Answer: (A), (B), (C)

Projectile motion of some thrown by hand on the surface of the earth will be approximately parabolic
Planets will not have elliptic orbits
Circular orbits of planets is not possible

If the law of gravitation become an inverse cube law then

$F=\frac{GMm}{r^3}=\frac{m{v}^2}{r}$

Or $V=\frac{\sqrt{GM}}{r}$

Time period of the revolution of the planet

$T=\frac{2\pi r}{V}$

$T=\frac{2\pi r^2}{\sqrt{GM}}$

$T^2\propto r^4$

It mean a planet will not have <br> an elliptical orbit. The circular orbit of a planet may not be possible as the gravitational attractive force obays inverse square law and not inverse cube law. A stone thrown by hand on the surface of the earth will follow nearly parabolic path, under the gravitational force. There will be some gravitational force inside a spherical shell of uniform density.