If the law of gravitation, 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  approximately parabolic
D. there will be no gravitational force inside as  spherical shell of uniform density

Answer

A, C

Explanation

`implies` Gravitational force = centripetal force,
`F = (GMm)/r^2 = (m^2)/r`
`:.` v = orbtial speed `=sqrt(GM)/r implies v prop 1/r`
Time period of revolution of planet,
`T= (2pir)/v = (2pir)/((sqrtGM)/r) = (2pir^2)/(sqrt(GM))`
`T^(2) prop r^4`
Hence, orbit will not be elliptical. [for elliptical orbit `T_2 prop r^3` ]
As force `F = ((GM)/r^2) m = gm `
where `g. = (GM)/r^2`
As g., acceleration due to gravity is constant, hence path followed by a projectile will be approximately parabolic.