The mass of planet B is 4m
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Newton's gravitational law states that the force of attraction between two objects can be formulated as follows:
[tex]\large {\boxed {F = G \frac{m_1 ~ m_2}{R^2}} }[/tex]
F = Gravitational Force ( Newton )
G = Gravitational Constant ( 6.67 × 10⁻¹¹ Nm² / kg² )
m = Object's Mass ( kg )
R = Distance Between Objects ( m )
Let us now tackle the problem !
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Given:
gravitational acceleration of Planet A = g₁ = g
gravitational acceleration of Planet B = g₂ = g
radius of Planet A = R₁ = R
radius of Planet B = R₂ = 2R
mass of Planet A = M₁ = m
Asked:
mass of Planet B = M₂ = ?
Solution:
We will compare the gravitational acceleration of the two planets as follows:
[tex]g_1 : g_2 = G\frac{M_1}{(R_1)^2} : G\frac{M_2}{(R_2)^2}[/tex]
[tex]g_1 : g_2 = \frac{M_1}{(R_1)^2} : \frac{M_2}{(R_2)^2}[/tex]
[tex]g : g = \frac{m}{(R)^2} : \frac{M_2}{(2R)^2}[/tex]
[tex]1 : 1 = m : \frac{1}{4}M_2[/tex]
[tex]\frac{1}{4}M_2 = m[/tex]
[tex]\boxed{M_2 = 4m}[/tex]
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Grade: High School
Subject: Physics
Chapter: Gravitational Fields
