If the radius of the earth becomes half of its present value but its density remains unchanged then find the weight of body on the surface of earth.

Explanation

`implies g =(GM_(e))/R_e^2=G/(R_e^2)(4/3piR_e^3rho)=4/3 piR_erho`
Since the radius becomes half,
`g. = 4/3 piG((R_e)/2)rho =1/2 (4/3 pi GR_erho)`
`:. g. =g/2 ` so weight becomes half
Weight `W prop g`
`:. (W.)/W = (g.)/g`
`:. W. = W xx 1/2`
` :. W. = W/2`