An astronaut on a strange planet finds that acceleration due to gravity is twice as that on the surface of Earth. Which of the following could explain this?

Question

An astronaut on a strange planet finds that acceleration due to gravity is twice as that on the surface of Earth. Which of the following could explain this? (A) Both the mass and radius of the planet are twice as that of Earth. (B) Mass of the planet is half as that of Earth, but radius is same as that of Earth. (C) Both the mass and radius of the planet are half as that of Earth. (D) Radius of the planet is half as that of Earth, but the mass is the same as that of Earth

Tardigrade Admin · Accepted Answer

Acceleration due to gravity on the surface of the planet is gp=(G Mp2/Rp2) Given, Mp=(Me/2) and Rp=(Re/2) ∴ gp=(G(M e / 2)/(R e / 2)2)=(2 G Me/Re)=2 ge

Q. An astronaut on a strange planet finds that acceleration due to gravity is twice as that on the surface of Earth. Which of the following could explain this?

Both the mass and radius of the planet are twice as that of Earth.

Mass of the planet is half as that of Earth, but radius is same as that of Earth.

Both the mass and radius of the planet are half as that of Earth.

Radius of the planet is half as that of Earth, but the mass is the same as that of Earth

Acceleration due to gravity on the surface of the planet is $g_{p} = \frac{G M _{p}^{2}}{R _{p}^{2}}$
Given, $M_{p} = \frac{M _{e}}{2}$
and $R_{p} = \frac{R _{e}}{2}$
$∴ g_{p} = \frac{G ( M e /2 )}{( R e /2 ) ^{2}} = \frac{2 G M _{e}}{R _{e}} = 2 g_{e}$

Q. An astronaut on a strange planet finds that acceleration due to gravity is twice as that on the surface of Earth. Which of the following could explain this?

Both the mass and radius of the planet are twice as that of Earth.

Mass of the planet is half as that of Earth, but radius is same as that of Earth.

Both the mass and radius of the planet are half as that of Earth.

Radius of the planet is half as that of Earth, but the mass is the same as that of Earth

Acceleration due to gravity on the surface of the planet is gp​=Rp2​GMp2​​ Given, Mp​=2Me​​ and Rp​=2Re​​ ∴gp​=(Re/2)2G(Me/2)​=Re​2GMe​​=2ge​

Acceleration due to gravity on the surface of the planet is $g_{p} = \frac{G M _{p}^{2}}{R _{p}^{2}}$
Given, $M_{p} = \frac{M _{e}}{2}$
and $R_{p} = \frac{R _{e}}{2}$
$∴ g_{p} = \frac{G ( M e /2 )}{( R e /2 ) ^{2}} = \frac{2 G M _{e}}{R _{e}} = 2 g_{e}$