A quantity is given by Q = X⁻² · Y³⁄² · Z⁻²⁄⁵. The fractional errors in X, Y and Z are 0.1, 0.2 and 0.5 respectively. The maximum fractional error in Q is:
Options

Question

A quantity is given by Q = X⁻² · Y³⁄² · Z⁻²⁄⁵. The fractional errors in X, Y and Z are 0.1, 0.2 and 0.5 respectively. The maximum fractional error in Q is:

G1 Physics · Accepted Answer

For a product of powers, the maximum fractional error is the sum of the absolute powers multiplied by the corresponding fractional errors. For Q = X⁻² · Y³⁄² · Z⁻²⁄⁵, ΔQ/Q = 2(ΔX/X) + (3/2)(ΔY/Y) + (2/5)(ΔZ/Z). Substitute: ΔQ/Q = 2(0.1) + (3/2)(0.2) + (2/5)(0.5) = 0.2 + 0.3 + 0.2 = 0.7. Correct option: C.