Question

${\huge {\bf {\red {\underline {\underline {Physics \: Question}}}}}}$
The force of gravity that acts on an object on the surface of Mars is 20 N. What force of gravity will act on the same object on the surface of the Earth? (use gravitational field strength g = 9.8 N/Kg on the surface of the Earth).
​

Answer 1

$\color{red}\huge{\underline{\underline{GIVEN\dag}}}$

• Force of 20N acts on a body on Mars due to gravity.

$\color{red}\huge{\underline{\underline{SOLUTION\dag}}}$

We know that;

Acceleration due to gravity on mars is $3.7m/s^{2}$

We also know that;

${\boxed{\color{blue}F=ma}}$

$\implies 20N=m(3.7ms^{-2})$

$\implies m=\frac{20}{(3.7ms^{-2})}$

$\color{orange}\therefore m(mass)=5.4Kg$

Force on earth;

$F=ma$

$F=(5.4kg)(9.8ms^{-2})$

${\boxed{\color{orange}\therefore F=52.9N}}$

HOPE THAT HELPS!!!

Answer 2

$\underline{\underline{\sf{\maltese\:\:Question}}}$

• The force of gravity that acts on an object on the surface of Mars is 20 N. What force of gravity will act on the same object on the surface of the Earth? (use gravitational field strength g = 9.8 N/Kg on the surface of the Earth)

$\underline{\underline{\sf{\maltese\:\:Given}}}$

• Force of gravity that acts on an object on the surface of Mars = 20 N

• Gravitational field strength g = 9.8 N/Kg (on the surface of the Earth)

$\underline{\underline{\sf{\maltese\:\:To\:Find}}}$

• What Force of gravity will act on the same object on the surface of the Earth

$\underline{\underline{\sf{\maltese\:\:Answer}}}$

• Force of gravity will act on the same object on the surface of the Earth is 53 N

$\underline{\underline{\sf{\maltese\:\:Calculations}}}$

Let :

• The gravitational field strength on Mars be gₘ

• The gravitational field strength on Earth be g and m (m is mass of object)

The acceleration is due to the universal force of gravity, therefore Newton's second law and the universal force of gravity are equal.

mgₘ = GMm/Rₘ² , on the surface of Mars

⇒ gₘ = GM/Rₘ²

Where :

• M ( 6.39 × 10²³ kg) is the mass of Mars

• Rₘ (3.39 × 10⁶ m) is radius of Mars.

On the surface of Mars

F = mgₘ and F = 20 N

m = F/gₘ = 20/gₘ

On the surface of the Earth

Fₑ = gₘ

= 9.8 × F/gₘ

= 9.8 × 20/(GM/Rₘ²)

= 9.8 × 20 × Rₘ²/(GM)

= 9.8 × 20 × (3.39 × 10⁶)² / (6.674 × 10⁻¹¹ × 6.39 × 10²³)

= 53 N