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Jobisdone [24]
3 years ago
12

The weight of an object is the same on two different planets. The mass of planet A is only sixty percent that of planet B. Find

the ratio of Ra/Rb of the radii of the planets.
Physics
1 answer:
natka813 [3]3 years ago
6 0

Answer:

0.775

Explanation:

The weight of an object on a planet is equal to the gravitational force exerted by the planet on the object:

F=G\frac{Mm}{R^2}

where

G is the gravitational constant

M is the mass of the planet

m is the mass of the object

R is the radius of the planet

For planet A, the weight of the object is

F_A=G\frac{M_Am}{R_A^2}

For planet B,

F_B=G\frac{M_Bm}{R_B^2}

We also know that the weight of the object on the two planets is the same, so

F_A = F_B

So we can write

G\frac{M_Am}{R_A^2} = G\frac{M_Bm}{R_B^2}

We also know that the mass of planet A is only sixty percent that of planet B, so

M_A = 0.60 M_B

Substituting,

G\frac{0.60 M_Bm}{R_A^2} = G\frac{M_Bm}{R_B^2}

Now we can elimanate G, MB and m from the equation, and we get

\frac{0.60}{R_A^2}=\frac{1}{R_B^2}

So the ratio between the radii of the two planets is

\frac{R_A}{R_B}=\sqrt{0.60}=0.775

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