Mars has a diameter of approximately 0.5 times that of Earth, and a mass of 0.1 times that of Earth. The surface gravitational field strength on Mars compared with that on Earth is greater by a factor of

Question

Mars has a diameter of approximately 0.5 times that of Earth, and a mass of 0.1 times that of Earth. The surface gravitational field strength on Mars compared with that on Earth is greater by a factor of (A) 0.1 (B) 0.2 (C) 0.4 (D) 2.0

Tardigrade Admin · Accepted Answer

At the surface, ge=(G M/R2) g text Mars =(G(0.1 M)/(0.5 R)2)=((0.1/0.52)) (G M/R2)=(2/5) ⋅ ge ⇒ g text Mars =0.4 g text Earth

Q. Mars has a diameter of approximately $0.5$ times that of Earth, and a mass of $0.1$ times that of Earth. The surface gravitational field strength on Mars compared with that on Earth is greater by a factor of

0.1

0.2

0.4

2.0

At the surface, $g_{e} = \frac{GM}{R ^{2}}$
$g_{Mars} = \frac{G ( 0.1 M )}{( 0.5 R ) ^{2}} = (\frac{0.1}{0. 5 ^{2}}) \frac{GM}{R ^{2}} = \frac{2}{5} \cdot g_{e}$
$\Rightarrow g_{Mars} = 0.4 g_{Earth}$

Q. Mars has a diameter of approximately 0.5 times that of Earth, and a mass of 0.1 times that of Earth. The surface gravitational field strength on Mars compared with that on Earth is greater by a factor of

0.1

0.2

0.4

2.0

At the surface, ge​=R2GM​ gMars ​=(0.5R)2G(0.1M)​=(0.520.1​)R2GM​=52​⋅ge​ ⇒gMars ​=0.4gEarth​

Q. Mars has a diameter of approximately $0.5$ times that of Earth, and a mass of $0.1$ times that of Earth. The surface gravitational field strength on Mars compared with that on Earth is greater by a factor of

At the surface, $g_{e} = \frac{GM}{R ^{2}}$
$g_{Mars} = \frac{G ( 0.1 M )}{( 0.5 R ) ^{2}} = (\frac{0.1}{0. 5 ^{2}}) \frac{GM}{R ^{2}} = \frac{2}{5} \cdot g_{e}$
$\Rightarrow g_{Mars} = 0.4 g_{Earth}$