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  • 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

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 a stone 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

Answers (1)

The correct answer is the option (a), (b), and (c).

We know that Force of gravitation = Centrifugal force for a body in a circular motion

If the law of gravitation becomes inverse cube law then

\frac{GmM}{r^{3}}=\frac{v^{2}m}{r}

where m = mass of the planet, M = mass of the sun and r = radius of the orbit

Thus, v is inversely proportionate to r

The time period of a planet around the sun =\frac{2\pi r}{v}

T^2\propto r^4

So the path is not elliptical. (By Keplers law T^2\propto r^3)

So, a is correct

When \frac{GmM}{r^{3}}=mg'

g'=\frac{GM}{r^{2}}

Hence, b is incorrect

Since, T\alpha r^{2} ; the path of the projectile will be parabolic. Thus, (c) is correct

Gravitational force is a universal force as it acts everywhere. Hence, (d) is incorrect

 

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infoexpert23

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