Question

The distance of Pluto from sun is 40 times than the distance of earth from sun. If the mass of earth and Pluto is same, then the ratio of gravitational force of sun on earth and Pluto is

Answer 1

Answer:

1:40

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Answer 2

The ratio of gravitational force of sun on earth and Pluto is 1600

Distance between pluto and sun  = 40 x distance of earth from sun.

• Let distance of earth from sun  = r

• Then distance of pluto from sun  = 40 r

Let mass of earth  = Me

Let mass of pluto = Mp

• Given Me = Mp = M

Let m be the mass of the sun

Gravitation force is given by F = $\frac{G M1 M2}{d^{2} }$

Therefore,

• Force of  sun on earth , Fe= G M1 M2 / r^2 = G Mm/$r^{2}$

Force of sun on pluto , Fp= G M m / $(40r)^{2}$ = G Mm /1600$r^{2}$

Ratio of Forces : Fe/Fp = 1600