A physical quantity z depends on four observables a, b, c and d , as z = a ^ 2 b ^ 2 / 3 c d ^ 3 . The percentage of error in the measurement of a, b, c and d are 2 % , 1 . 5 % , 4 % and 2 . 5 % respectively. The

Correct answer: D. 14 . 5 % ( )/(t) = (2 )/(a) + (2)/(3)( )/(b) + (1)/(2)( )/(c) + 3( )/(d) = 2 × 2 + (2)/(3) × 1 . 5 + (1)/(2) × 4 + 3 × 2 . 5 = 4 + 1 + 2 + 7 . 5 = 14 . 5 %

JEE Main 20205 SeptemberMorning Shift

Exam: JEE Main
Year: 2020
Date: 5 September
Shift: Morning Shift
Subject: Physics
Chapter: Mathematics in Physics

JEE Main 2020 · 5 September · Morning Shift · Physics · Mathematics in Physics

A physical quantity z depends on four observables a, b, c and d ,...

A physical quantity z depends on four observables

a, b, c

and

d

, as

z = \dfrac{{a}^{2}{b}^{2 / 3}}{\sqrt{c}{d}^{3}} .

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 :

Options

A $12 . 25 %$
B $16 . 5 %$
C $13 . 5 %$
D $14 . 5 %$

Correct answer

D. $14 . 5 %$

Step-by-step solution

$\dfrac{\Deltat}{t} = \dfrac{2\Deltaa}{a} + \dfrac{2}{3}\dfrac{\Deltab}{b} + \dfrac{1}{2}\dfrac{\Deltac}{c} + 3\dfrac{\Deltad}{d}$

$= 2 \times 2 + \dfrac{2}{3} \times 1 . 5 + \dfrac{1}{2} \times 4 + 3 \times 2 . 5$

$= 4 + 1 + 2 + 7 . 5$

$= 14 . 5 %$

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