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Question

A planet has a miss of eight times the mass of earth and density is also equal to eight times the average density of the earth. If g be the acceleration due to earth's gravity on its surface, then acceleration due to gravity on planet's surface will be :

A
2g
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B
4g
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C
8g
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D
16g
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Solution

The correct option is C 8g

Let the density of the planet is Dp, the density of the earth is De, the mass of the planet is Mp and the mass of the earth is Me.

The density of the planet is given as,

Dp=8De

Mp43πRp3=8×Me43πRe3

8Me43πRp3=8×Me43πRe3

Rp=Re

The acceleration due to gravity is given as,

gpge=GMpRp2GMeRe2

gpg=8×GMeRp2GMeRe2

gp=8g

Thus, the acceleration due to gravity on the planet’s surface is 8g.


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