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There are two planets A and B. They revolve around the sun in circular orbits. The orbital radius of A around the sun is twice that of orbital radius of B. The mass of A is twice that of mass of B. Compares the forces of gravitation between A to the sun and B to the sun.

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1:1

1:2

2:1

2:2

answer is B.

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Detailed Solution

Given that, as per question,

m_{A}

= 2

m_{B}

and

r_{A}

= 2

r_{B}

Let, Mass of the sun = M
Force of gravitation between A to the sun,

F_{As}

\frac{GM m_{A}}{(r_{A})^{2}}

Force of gravitation between B to the sun,

F_{Bs}

\frac{GM m_{B}}{(r_{B})^{2}}

On dividing both A and B, we get

\frac{F_{As}}{F_{Bs}}

(\frac{m_{A}}{m_{B}})

(\frac{r_{B}}{r_{A}})

(\frac{{2 m}_{B}}{m_{B}})

(\frac{r_{B}}{{2 r}_{B}})

\frac{1}{2}

So, the force of gravitation between A to the sun and B to the sun is 1:2.

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