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

Options

A. planets will not have elliptic orbits.
B. circular orbits of planets is not possible.
C. projectile motion of a stone thrown by hand on the surface of the earth will be appoximately perabolic.
D. there will be no gravitational force inside a spherical shell of uniform density.

Answer

A, B, C

Explanation

If the law of gravitational becomes an inverse cube law then `F = (GMm)/(r^(3)) = (m upsilon^(2))/(r )` or `upsilon = (sqrt(GM))/(r )`
`:.` Time period of revolution of a planet, `T = (2 pi r)/(upsilon) = (2 pi r^(2))/(sqrt(GM))` or `T^(2) prop r^(4)`. It mean a planet will not have
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.