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The earth's radius is about 6400 km, and the radius of mars is about 3200 km. The mass of the earth is about 10 times the mass of mars. An object weighs 200 N on the surface of the earth. What is the weight of the same object on the surface of mars?

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60 N

80 N

30 N

9 N

answer is B.

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Detailed Solution

The weight of the object on the surface of the mars is

80 N

Given:
Weight of object on Earth

= 200 N

Radius of Earth

= 6400 km

The radius of Mars

= 3200 km

Mass of Earth (M_{E}) = 10 \times Mass of Mars (M_{M})

Value of

g

on the earth,

g_{E} = \frac{G M_{E}}{R_{E}^{2}}

(Where

g_{E}

is the gravity acceleration of earth, and

R_{E}

is the radius of earth)
Value of

g

on mars,

g_{M} = \frac{G M_{M}}{R_{M}^{2}}

(Where

g_{M}

is the gravity acceleration of mars, and

R_{M}

is the radius of mars)
Now,

\frac{W_{M}}{W_{E}} = \frac{g_{M}}{g_{E}}

(Where

W_{M}

is the weight of mars and

W_{E}

is the weight of earth)

\Rightarrow \frac{W_{M}}{W_{E}} = \frac{M_{M}}{M_{E}} \times {(\frac{R_{E}}{R_{M}})}^{2}

\Rightarrow \frac{W_{M}}{W_{E}} = \frac{1}{10} \times 2^{2}

\Rightarrow \frac{W_{M}}{W_{E}} = \frac{4}{10}

\Rightarrow \frac{W_{M}}{W_{E}} = \frac{2}{5}

\Rightarrow W_{M} = W_{E} \times \frac{2}{3}

\Rightarrow W_{M} = 200 \times \frac{2}{5}

\Rightarrow W_{M} = 80 N

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