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Is it true that the weight of a body on the surface of the earth is $392 N$ . what will be the weight of this body on a planet whose mass is doubled that of the earth and radius is four times that of the earth?

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49 N

60 N

None of the above

answer is B.

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Detailed Solution

The weight of the body on that planet will be

49 N

.
Given data and assumptions:
Weight of the body on the earth,

W_{e} = 392 N

Mass of the planet,

M_{P} = 2 M_{e}

Radius of the planet,

R_{p} = 4 R_{e}

where,

M_{e}

is the mass of the earth, and

R_{e}

is the radius of the earth.
We know that the acceleration due to gravity on earth,

g = \frac{G M_{e}}{{R_{e}^{2}}^{}}

Where

G

is the universal gravitational constant.
Now, the acceleration due to gravity on the planet,

g_{p} = \frac{G \times 2 M_{e}}{(4 R_{E})^{2}}

\Rightarrow

= \frac{G M_{e}}{{8 R}_{e}^{2}^{}}

\Rightarrow

g_{p} = \frac{g}{8}

So the weight of the body on the planet would be,

W_{p} = \frac{392}{8}

= 49 N

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