A perfectly adjusted beam balance together with its standard weights is taken from sea level to the top of a hill where the acceleration due to gravity decreases by 0.5%. The arms of the balance are equal and its centre of gravity lies exactly below the knife-edge.
(i) Show mathematically that a body which balances 200g of standard weights at sea level will still balance the same weights at the hill.
(ii) If the same body is weighed with a spring balance that was calibrated at sea level, calculate the percentage error in the reading obtained at the hill.
(iii) On the basis of your results, explain why the beam balance is preferred over the spring balance for determining mass at different locations on Earth.