Question

Q16.A physical quantity P is related to four observables a, b, c and d as follows : P= ( a³b²)/( c½d½) The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and 2%, respectively. What is the percentage error in the quantity P ? If the value of P calculated using the above relation turns out to be 3.763, to what value should you round off the result ?​

Answer 1

Answer:

13%, 3.8

Explanation:

taking log on both sides,

logP = 3loga + 2logb - 1/2logc - logd

differentiating both sides,

∆P/P = 3∆a/a + 2∆b/b - 1/2∆c/c - ∆d/d

But errors are always added and never substracted, so,

∆P/P = 3∆a/a + 2∆b/b + 1/2∆c/c + ∆d/d

∆P/P = 3×1 + 2×3 + 1/2×4 + 2

∆P/P = 13%

The value of P can be rounded off to nearest decimal point,

P = 3.8