Question

The radius of planet a is half the radius of planet b. If the mass of a is ma, what must be the mass of b so that the value of G on b is half that of its value of a?

Answer 1

From the question:

rA=rB2rA=rB2 (1)

gB=gA2gB=gA2 (2)

From the laws of Physics:

gA=GmArA2gA=GmArA2 (3)

gB=GmBrB2gB=GmBrB2 (4)

Replacing (3) and (4) in (2):

GmBrB2=GmA2rA2GmBrB2=GmA2rA2

mBrB2=mA2rA2mBrB2=mA2rA2 (5)

Replacing (1) in (5):

mBrB2=mA2(rB2)2mBrB2=mA2(rB2)2

mB=2mA

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Answer 2

Answer:

The mass of planet B must be twice that of the planet A.

Explanation:

See the attachment.

NOTE : The value of 'G' is constant and called as Universal Gravitational Constant. In question, 'g' is used which is 'acceleration due to gravity'.