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The earth's radius is about, $6400 km$ and that of mass 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 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 mass is

80 N .

Given:
The weight of an object on Mars

W_{M} = 200 N

Radius of Earth

R_{E} = 6400 km

Radius of Mars

R_{M} = 3200 km

And the mass of the earth is about

10

times the mass of mars.
At the surface of the earth,

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

……

(1)

Here,

g_{E =}

gravitational acceleration,

M_{E} =

mass of the earth,

R_{E} =

radius of the earth and

G =

universal gravitational constant.
Multiplied by mass

' m'

in equation (1) we get,

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

\Rightarrow W_{E} = \frac{G M_{E} m}{R_{E}^{2}}

….

(2)

(∵

w = mg)

Here,

W_{E}

is the weight of the object on earth.
Similarly, at the surface of mars,

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

Where,

g_{M =}

gravitational acceleration of mars,

M_{M} =

mass of the mars,

R_{M} =

radius of the mars and

G =

universal gravitational constant.

W_{M} = \frac{G M_{M} m}{R_{M}^{2}}

…

(3)

Here,

W_{M}

is the weight of the object on the surface of mars.
Now, divide equation

(3)

by equation

(2)

\frac{W_{M}}{W_{E}} = \frac{m g_{M}}{m g_{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}{5}

\Rightarrow

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

\Rightarrow

W_{M} = 80 N

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The earth's radius is about, 6400 km and that of mass 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 object on the surface of mars?

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The earth's radius is about, $6400 km$ and that of mass 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 object on the surface of mars?