A body weighs 200 N on the surface of the earth. How much will it weigh half way down to the centre of the earth? [NEET 2019]

Given, weight of the body, ω = 200 NAs we know ω = mg, where m is the mass of the body and B (= 10 ms-2) is acceleration due to gravity of the body at the surface of the earth.Since, mass m remains constant irrespective of the position of the body on the earth. However, B is not constant and its value at a depth d below the earth's surface is given as               g=g1-dR                        ... (i)where, R is the radius of the earth.Multiplying m on both sides of Eq. (i), we getmg'=mg1-dRNow, the weight of the body at half-way down  i.e. d=R2 to the centre of the earth ismg'=200×1-R/2R=2001-12=200×12=100 N∴  The body will weigh 100 N half-way down to the centre of the earth.