A physical quantity z depends on four observables a ,   b ,   c and d , as z = a 2 b 2 / 3 c d 3 .…

A physical quantity z depends on four observables a, b, c and d, as  z=a2b2/3cd3. The percentage of error in the measurement of a, b, c and d are 2%,1.5%,4%  and 2.5% respectively. The percentage of error in z is :
  1. 12.25%
  2. 16.5%
  3. 13.5%
  4. 14.5%

Solution

Δtt=2Δaa+23Δbb+12Δcc+3Δdd

=2×2+23×1.5+12×4+3×2.5

=4+1+2+7.5

=14.5%

Asked in: JEE Main 2020 (05 Sep Shift 1)

Practice more Mathematical Methods questions on Aicharya