Question

If you stood on a planet having a mass four times that of earth mass and a radius two times of earth radius , you would weigh?

Answer 1

Answer: Weight will remain same as on the Earth

Explanation :

From Universal law of gravitation :

$F=G\dfrac{M_em}{R^2}$......(1)

$M_e$ is the mass of earth

m is the mass of the person

R is the radius of the earth

We know that F= mg.....(2)

So, from equation (1) and (2)

$mg=\dfrac{GM_em}{R^2}$

$g=\dfrac{GM_e}{R^2}$.....(3)

It is given that, If we stood on a planet having a mass four times that of earth mass and a radius two times of earth radius then from equation (3)

$g=\dfrac{G\times 4M_e}{4R^2}$

The value of g is will not change. So, our weight would not change. It would remain the same as on the Earth.

Answer 2

The weight of the astronaut on the planet will be the same as on the Earth.

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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:

mass of Earth = M₁ = M

mass of Planet = M₂ = 4M

radius of Earth = R₁ = R

radius of Planet = R₂ = 2R

Asked:

weight of the astronaut on planet = w₂ = ?

Solution:

We will compare the weight of the astronaut on planet and earth as follows:

$w_2 : w_1 = mg_2 : mg_1$

$w_2 : w_1 = g_2 : g_1$

$w_2 : w_1 = G\frac{M_2}{(R_2)^2} : G\frac{M_1}{(R_1)^2}$

$w_2 : w_1 = G\frac{4M}{(2R)^2} : G\frac{M}{(R)^2}$

$w_2 : w_1 = G\frac{4M}{4R^2} : G\frac{M}{R^2}$

$w_2 : w_1 = G\frac{M}{R^2} : G\frac{M}{R^2}$

$w_2 : w_1 = 1 : 1$

$\large {\boxed {w_2 = w_1}}$

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From information above, we could conclude that the weight of the astronaut on the planet will be the same as on the Earth.

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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