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Question

Find the relation between the gravitational field on the surface of two planets A and B of masses mA,mB and radii RA and RB, respectively, if
a. they have equal mass,
b. they have equal (uniform) density.

A
a. For mA=mB,EAEB=R2BR2A
b. For ρA=ρB,EAEB=RA3RB.
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B
a. For mA=mB,EAEB=R2BR2A
b. For ρA=ρB,EAEB=RARB.
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C
a. For mA=mB,EAEB=R2BR2A
b. For ρA=ρB,EAEB=2RARB.
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D
a. For mA=mB,EAEB=R2BR2A
b. For ρA=ρB,EAEB=2RA2RB.
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Solution

The correct option is A a. For mA=mB,EAEB=R2BR2A
b. For ρA=ρB,EAEB=RARB.
Let EA & EB be tje gravitational field intensity on surface of A and B, then
EA=GMAR2A=G43πR3AρAR2A=4GπρARA3
Similarly, EB=GMBR2B=4GπρBRB3
a) If mA=mB
EAEB=R2BR2A
b) For ρA=ρB
EAEB=RARB

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