Question

(i) Solve the following problem :
The radius of planet A is half the radius of planet B. If the mass of A is
MĀ, what must be the mass of B so that the value of g on B is half that of
its value on A?​

Answer 1

Answer:

Given: Radius of planet A is half radius of planet B.

RA*= 1/2 RB*

i.e. RB*=2RA*

Value of gravity on planet B is half that on planet A.

gB*=1/2 gA*

i.e. gA*=2gB*

Mass of planet A = MA*

Mass of planet B = MB*=?

g =GM/R^2

gA* = GMA*/RA*^2 ..........(1)

gB* = GMB*/RB*^2 ..........(2)

Dividing (1) by (2)

gA*/gB*=GMA*/RA*^2÷GMB*/RB*^2

gA*/gB* =GMA*/RA*^2×RB*^2/GMB*

2GB*/GB*=GMA*/RA*^2×(2RA*)^2/GMB* ...........(GIVEN)

2=MA*/RA*^2×4RA*^2/MB*

2=4MA*/MB*

2MB*=4MA*

÷ BY 2,

MB*=2MA*

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