Question

how will the weight of a body change if radius of the earth becomes 1/4th of it's value, without changing it's mass​

Answer 1

Answer:

Hope,its help you

Explanation:

At surface of the Earth, weight Ws=R2GMm

At height, h of the Earth weight Wh=(R+h)2GMm

Now, 

Wh=4Ws

(R+h)2GMm=4R2GMm

R+h1=2R1

R+h=2R

h=R

Answer 2

Answer: 16 times

Explanation:

Weight = mass x acceleraction due to gravity (g)

The mass is same as given.

so g initially was:

g = GM/R^2 ———- 1

here R is the radius.

the radius becomes 1/4 x R.

so g finally is:

x = GM/(1/4 x R)^2

  = GM/1/16 x R^2 ——— 2

By dividing both statements:

g/x = GM/R^2 divided by GM/ 1/16 R^2

GM and R square will get cancelled

g/x = 1/16

16g = x

therefore the weight of the  new body will change:

16 times than the initial weight.