Question

a ratio of masses of two planets is 2:3 and the ratio of their radii is 4:7.
find the ratio of their acceleration due to gravity ​

Answer 1

Answer:

49:24

Explanation:

Please give me a thank you and follow me

Answer 2

• $\sf\dfrac{g_1}{g_2}$ = $\sf\dfrac{49}{24}$

Explanation:

Given,

• The ratio of masses of two planets, $\sf{M_1\:{:}\:M_2}\:=\:{2\:{:}\:3}$
• The ratio of radii of two planets, $\sf{R_1\:{:}\:R_2}$

We know that,

Gravity (g) = $\sf\dfrac{GM}{R_2}$

⟶ $\sf\dfrac{g_1}{g_2}$= $\sf{\dfrac{\dfrac{GM_1}{R_1^2}}{\dfrac{GM_2}{R_2^2}}}$

⟶ $\sf\dfrac{g_1}{g_2}$= $\sf{\dfrac{GM_1}{R_1^2}}\:×\:{\dfrac{R_2^2}{GM_2}}$

⟶ $\sf\dfrac{g_1}{g_2}$= $\sf{\dfrac{{\cancel{G}}M_1}{R_1^2}}\:×\:{\dfrac{R_2^2}{{\cancel{G}}M_2}}$

⟶ $\sf\dfrac{g_1}{g_2}$= $\sf{\dfrac{M_1}{M_2}}{\dfrac{R_2^2}{R_1^2}}$

⟶ $\sf\dfrac{g_1}{g_2}$= $\sf{\dfrac{2}{3}}{\dfrac{7^2}{42}}$

⟶ $\sf\dfrac{g_1}{g_2}$ = $\sf\dfrac{2\:×\:49}{3\:×\:16}$

⟶ ∴ $\sf\dfrac{g_1}{g_2}$ = $\sf\dfrac{49}{24}$