In an experiment to measure the centripetal force acting on a particle moving in a circular path, the mass of the particle is measured as (50 0.5) g , its velocity as (20 0.4) m/s , and the radius of the circular path as (10 0.3) cm . The maximum percentage error in the calculated value of the centripetal force will be

Step-by-step solution

The formula for centripetal force is given by F = mv^2 r The maximum percentage error in the calculation of force is F F 100 = ( m m + 2 v v + r r ) 100 First, calculate the individual percentage errors: Percentage error in mass = 0.5 50 100 = 1 % Percentage error in velocity = 0.4 20 100 = 2 % Percentage error in radius = 0.3 10 100 = 3 % Substitute these values into the error equation: F F 100 = 1 % + 2(2 %) + 3 % F F 100 = 1 % + 4 % + 3 % = 8 % Answer: 8 %