Question

5. There are two planets X and Y. The mass
of Y is twice the mass of X and the radius
of Y is half the radius of X. Find the
ratio of acceleration due to gravity on the
two planets.​

Answer 1

Explanation:

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Answer 2

Answer:

1/2

Explanation:

let M and M' be the mass of X and Y planet. let R and R' be the radius of X and Y planet.

according to question

M' = 2 M ----------- ( 1 )

and

R' = 1/2 R -------------( 2 )

now let g and g' be acceleration due to gravity on the planets X and Y

then

g = GM/R^2 ------------ (3)

and

g' = GM'/R'^2 ---------(4)

dividing (3) and (4)

g/g' = (GM/R^2) / (GM'/R'^2)

g/g' = (M/R^2) * (R'^2/M')

= (M/R^2) * (1/4R^2 / 2M) ( from (1) and (2) )

g/g' = 1/2

since masser the planet more will be its gravity, more the size lesser will be the gravity.

g/g' = 1/2

which means

g' = 2g

that is planet Y is twice the mass of planet X but 1/2 the radius of X, that's why gravity is more in Y