the centripetal force F= mv²/r , the mass , velocity and circular path of an object are 0.5 kg, 10m/s and 0.4m respectively . Find the % error on the force given m, v, and r are measured to accuracies of 0.005kg , 0.01 m/s and 0.01m respectively.

Given the centripetal force formula:

F = (m * v²) / r

where:
m = 0.5 kg (± 0.005 kg)
v = 10 m/s (± 0.01 m/s)
r = 0.4 m (± 0.01 m)

Step 1: Calculate the absolute value of the force
F = (0.5 * 10²) / 0.4
= (0.5 * 100) / 0.4
= 50 / 0.4
= 125 N

Step 2: Find the relative errors
The general formula for relative error in a product or quotient is:

ΔF / F = (Δm / m) + 2(Δv / v) + (Δr / r)

Substituting the given values:

Δm / m = 0.005 / 0.5 = 0.01
Δv / v = 0.01 / 10 = 0.001
Δr / r = 0.01 / 0.4 = 0.025

Now, calculating the total relative error:

ΔF / F = (0.01) + 2(0.001) + (0.025)
= 0.01 + 0.002 + 0.025
= 0.037

Step 3: Convert relative error to percentage
% error = (ΔF / F) * 100
= 0.037 * 100
= 3.7%

Final Answer:
The percentage error in the force is 3.7%.