Question

If the earth shrinks to 50% of it's real radius ,it's. Mass remaining the same, the weight of the body on the earth will increase by 50% or decrease by50%?

Answer 1

your question is incomplete. A complete question is ---> If the earth shrinks half in radius its mass remaining the same, then by what % will the weight of the object on earth change?

A)decreases by 50% B)increases by 50% C)decreases by 25% D)increases by 300%

answer : option (D) increases by 300%

explanation : weight of the object is given by, W = mg, where g is acceleration due to gravity.

and we know as well, acceleration due to gravity is inversely proportional to r² [i.e., g = GM/r² ]

so, if earth shrinks to 50% of its real radius. acceleration due to gravity become 4 times of its initial value.

then, weight of object becomes 4 times. i.e. W' = 4mg

so, percentage increase = (4mg -mg)/mg × 100 = 300%

hence, option (D) is correct choice.

Answer 2

Weight will increase by 50•/•.

Explanation:

R' is your new radius.

So R' = R/2

Where R is the original radius of the earth. We all know that acceleration due to gravity is inversely proportional to square of the radius of the earth.so when the radius is decreased by half, then the acceleration due to gravity will increase by half.

g = GM/R^2

Substitute R' in R

g = GM/R'^2

g = GM/R'^2/4

since they are inversely proportional multiply g with 1/2.

g/2 = GM/R'/4

g/2 ✖ 4 = GM/R'^2

g ✖ 2 = GM/R'^2

GM/R'^2 can also be written as g.

So g' = g ✖ 2

So g is increased by half then the weight will also increase by half.

W = mg

Substitute any value in mass and the value of g is increased by half. So g = 19.6. Original value of g = 9.8

Substitute both the values and find the difference between the two masses. And then find the percentage of the difference.Hence It will be increased by half.I mean 50•/•...