Question

38. A physical quantity is represented by X = [MaLbT-c]. If percentage error in the measurement of M, L and T are α%, ß% and ¥% respectively, then maximum percentage error in measurement of X should be (Given that α, ß and ¥ are very small) (1) (αa - βb + ¥c)% (2) (αa + βb + ¥c)% (3) (αa - βb - ¥c)% (4) (αa + βb – ¥c)% ​

Answer 1

Answer:

0ption 3) (αa + βb + γc ) %

Explanation:

X = [$M^{a}$$L^{b}$$T^{-c}$]

Error in measurement of X is

ΔX/X = a (ΔM/M) + b (ΔL/L) + c (ΔT/T)

percentage errors are

(ΔX/X) x 100 = a (ΔM/M) x 100 + b (ΔL/L) x 100 + c (ΔT/T) x 100

                     = (aα + bβ + cγ ) %