Q.

Calculate the value of acceleration due to gravity on a planet whose mass and radius are 2 times that of the earth. 

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a

0.5 g

b

2 g

c

0.25 g

d

1 g

answer is B.

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Detailed Solution

Consider, 
ge = Acceleration due to gravity on the earth
gp = Acceleration due to gravity on the given planet
Me = Mass of the earth
Re = Radius of the earth
Mp = Mass of the planet
Rp = Radius of the planet

Acceleration due to the gravity at the surface of the earth is:

ge=GMeRe2

It is given that Mp=2Me,Rp=2Re

Acceleration due to the gravity at the surface of the planet: 

gp=GMpRp2=G(2Me)(2Re)2 

gp=GMe2Re2=ge2

gp=ge2= 0.5 ge

gp= 0.5 ge

Therefore, the acceleration due to gravity on the planet will be 0.5 g that is half the value of the g on the earth.

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