Question

For two planets, ratio of their radii is 1:2 and the ratio of their masses is 2:3. Find the ratio of weights of a body on these planets.

Answer 1

this is the answer hope it helps

Answer 2

Given that,

Ratio of the radii is 1:2 and the ratio of their masses is 2:3.

To find,

The ratio of weights of a body on these planets.

Solution,

Let $g_1\ and\ g_2$ area the acceleration due to gravity on two planets. It is is given by using Newton's law of gravitation as :

For planet 1 weight is,

$W_1=\dfrac{Gm_1M}{r_1^2}$ .......(1)

For planet 2 weight is ,

$W_2=\dfrac{Gm_2M}{r_2^2}$ ......(2)

Dividing equation (1) and (2) we get :

$\dfrac{W_1}{W_2}=\dfrac{m_1r_2^2}{m_2r_1^2}$ ......(3)

Since,

$\dfrac{m_1}{m_2}=\dfrac{2}{3}\\\\\dfrac{r_1}{r_2}=\dfrac{1}{2}$

Equation (3) becomes :

$\dfrac{W_1}{W_2}=\dfrac{2\times (2)^2}{3\times (1)^2}\\\\\dfrac{W_1}{W_2}=\dfrac{8}{3}$

So, the ratio of weights of a body on these planets is 8:3.

Learn more,

Gravitational force

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