Question

if the earth shrinks 50% of its real radius its mass remaining the same the weight of a body on the earth will be what ?​

Answer 1

Let radius of earth is R .

then, acceleration due to gravity on the earth's surface is given by,

and then, weight of body of mass m, is W = mg

a/c to question, The earth shrinks 50% of its real radius .

e.g., new radius , R' = 50% of R = R/2

then, acceleration due to gravity on the earth's surface is given by,

or,

then, weight of body of mass m will be W' = mg' = mg/4

hence, weight of body will be (1/4)th of weight of body when radius of earth is real.