Two identical blocks of mass m are suspended from a beam balance whose scale pans differ in vertical height by h ≪ R , If R and ρ are the radius and density of the earth, then the error in weighing is

Step-by-step solution

As with height g varies as and in accord with the figure h 1 > h 2 so W 1 will be lesser than W 2 and W 2 - W 1 = mg 2 - mg 1 = 2 mg h 1 R - h 2 R or W 2 - W 1 = 2 m GM R 2 h R as g = GM R 2 and h 1 - h 2 = h or W 2 - W 1 = 2 mhG R 3 4 3 πR 3 ρ = 8 3 πρGmh as M = 4 3 πR 3 ρ