The gravitational field strength at the surface of a certain planet is g. Which of the following is the gravitational field strength at the surface of a planet with twice the radius and twice the mass?

Question

The gravitational field strength at the surface of a certain planet is g. Which of the following is the gravitational field strength at the surface of a planet with twice the radius and twice the mass? (A) g/2 (B) g (C) 2g (D) 4g

Tardigrade Admin · Accepted Answer

For a given planet, g = (GM/R2) Gravitational field strength at the surface of another planet, g' = (GM'/R'2) Here, M' = 2M , R' = 2R ∴ : :: g' = (G(1M)/(2R)2) = (g/2)

Q. The gravitational field strength at the surface of a certain planet is $g$ . Which of the following is the gravitational field strength at the surface of a planet with twice the radius and twice the mass?

$g /2$

$g$

$2 g$

$4 g$

For a given planet, $g = \frac{GM}{R ^{2}}$
Gravitational field strength at the surface of another planet, $g^{'} = \frac{G M ^{'}}{R ^{'2}}$
Here, $M^{'} = 2 M, R^{'} = 2 R$
$∴ g^{'} = \frac{G ( 1 M )}{( 2 R ) ^{2}} = \frac{g}{2}$

Q. The gravitational field strength at the surface of a certain planet is g. Which of the following is the gravitational field strength at the surface of a planet with twice the radius and twice the mass?

g/2

g

2g

4g

For a given planet, g=R2GM​ Gravitational field strength at the surface of another planet, g′=R′2GM′​ Here, M′=2M,R′=2R ∴g′=(2R)2G(1M)​=2g​

Q. The gravitational field strength at the surface of a certain planet is $g$ . Which of the following is the gravitational field strength at the surface of a planet with twice the radius and twice the mass?

$g /2$

$g$

$2 g$

$4 g$

For a given planet, $g = \frac{GM}{R ^{2}}$
Gravitational field strength at the surface of another planet, $g^{'} = \frac{G M ^{'}}{R ^{'2}}$
Here, $M^{'} = 2 M, R^{'} = 2 R$
$∴ g^{'} = \frac{G ( 1 M )}{( 2 R ) ^{2}} = \frac{g}{2}$