The pressure on a square plate is measured by measuring the force acting on the plate and length of the sides of the plate. The maximum error in the measurement of force and length are respectively 4 % and 2 % , the percentage error in the measurement of pressure is

Step-by-step solution

The pressure P on a square plate is defined as the force F divided by its area A = L^2 where L is the side length, giving P = F L⁻² . For a quantity Z = X^a Y^b , the maximum percentage error is given by: Z Z 100 % = a ( X X 100 % ) + b ( Y Y 100 % ) Applying this to P = F^1 L⁻² : P P 100 % = 1 ( F F 100 % ) + 2 ( L L 100 % ) Given F F 100 % = 4 % and L L 100 % = 2 % , substitution yields: P P 100 % = 4 % + 2 2 % = 4 % + 4 % = 8 % Answer: D