Question

The masses of two planets are in the ratio 4 : 2. Their radii are in the ratio 2 : 4. The acceleration due to gravity on the planets are in the ratio

Answer 1

Answer:

The acceleration due to gravity on the planets are in the ratio, $g_1:g_2=8:1$      

Explanation:

Acceleration due to gravity is given by,

            $g=\frac{GM}{R^2}$

The masses of two planets are in the ratio m1:m2 = 4:2

The radii are in the ratio R1:R2 = 2:4

Acceleration due to gravity is directly proportional to mass and inversely proportional to the square of the radius.

The acceleration due to gravity on the planets are in the ratio,

          $\frac{g_1}{ g_2}=\frac{m_1}{m_2}\times \frac{R_2^2}{R_1^2}=\frac{4}{2}\times \frac{4^2}{2^2}=\frac{8}{1}$

           $g_1:g_2=8:1$