If the present radius of the earth is doubled keeping the mass unchanged, how will the weight of a body on the surface of the earth change ?

Explanation

Weight of a body of mass m on the earth.s surface , `W =mg=(GMm)/(R^2)` where M and R are the mass and the radius of the earth.
when mass remains constant and radius doubles, then weight `W_1=(GMm)/((2R)^2)=(GMm)/(4R^2)`
`therefore (W_1)/W=(GMm)/(4R^2)*(R^2)/(GMm) =1/4`
Hence, new weight would be `1/4` th of the present weight.