Question

Two planets have the same surface gravity, but planet b has twice the radius of planet

Answer 1

The mass of planet B is 4m

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Further explanation

Newton's gravitational law states that the force of attraction between two objects can be formulated as follows:

$\large {\boxed {F = G \frac{m_1 ~ m_2}{R^2}} }$

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:

$g_1 : g_2 = G\frac{M_1}{(R_1)^2} : G\frac{M_2}{(R_2)^2}$

$g_1 : g_2 = \frac{M_1}{(R_1)^2} : \frac{M_2}{(R_2)^2}$

$g : g = \frac{m}{(R)^2} : \frac{M_2}{(2R)^2}$

$1 : 1 = m : \frac{1}{4}M_2$

$\frac{1}{4}M_2 = m$

$\boxed{M_2 = 4m}$

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Learn more

• Impacts of Gravity : brainly.com/question/5330244
• Effect of Earth’s Gravity on Objects : brainly.com/question/8844454
• The Acceleration Due To Gravity : brainly.com/question/4189441

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Answer details

Grade: High School

Subject: Physics

Chapter: Gravitational Fields

Answer 2

Planet A;
m = the mass 
Let r =  the radius 

Planet B:
Let M =  the mass
The radius is 2r (twice the radius of planet A)

The surface gravitational acceleration of planets A and B (they have the same surface gravity) are
$g= \frac{Gm}{r^{2}} \, and \, g= \frac{GM}{(2r)^{2}} \\\\ m= \frac{M}{4} \\\\ M=4m$

Answer: The mass of planet B is 4m.