IIT JEE , AIEEE Forum - Physics , Mechanics

hardcore_genius

Suppose that silver surfer comes to earth & he invites galactus to the earth.Galactus sucks up matter from earth decreasing its density to 1/4 of its true value.Due to the decrease in its density , the earth expands ( due to decrease in gravitational pull). Find its new radius R' & new acceleration due to gravity g' ?????????

swashata4iit

How can mass volume and density change? If the volume of the earth remains the same then there's a chance that the density will decrease. But in the question out of the three variable u have one known and 3 unknown. How can u solve it?

hardcore_genius

Hey yaar, as volume is increasing & density is decreasing, this straightly means that mass is constant.Now, i think it's simple!!!

swashata4iit

If mass is kept constant then the answer goes like follows:

On solving this problem we take the earth to be a homogenous sphere so that its C.M may be taken at its geometrical centre.

Let the new radius be R and the original radius be r.

As M=mass of earth = contant

4/3

r³

= 4/3

R³

/4

or, R = r^{[ 3]}

4

Let the new surface acc due to gravity be g

Hence from newton's 2nd law of motion and law of gravitation we have

g = [4/3

R³

/4]/R²

or g = 4^{[ 3]}

4/3

R

Plz tell me if I'm correct and plz vote my efforts

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