JEE MAIN - Physics (2018 - 16th April Morning Slot - No. 21)
The percentage errors in quantities P, Q, R and S are 0.5%, 1%, 3% and 1.5% respectively in the measurement of a physical quantity A = $${{{P^3}{Q^2}} \over {\sqrt R S}}.$$
The maximum percentage error in the value of A will be :
The maximum percentage error in the value of A will be :
6.0%
7.5%
8.5%
6.5%
Explanation
Given,
A = $${{{P^3}{Q^2}} \over {\sqrt R S}}$$
$$\therefore\,\,\,\,$$ $${{\Delta A} \over A}$$ = 3 $${{\Delta P} \over P}$$ + 2 $${{\Delta Q} \over Q}$$ + $${1 \over 2}$$ $${{\Delta R} \over R}$$ + $${{\Delta S} \over S}$$
Maximum percentage error in the value of A is
$${{\Delta A} \over A}$$ $$ \times $$ 100 = 3 $$ \times $$ 0.5 + 2 $$ \times $$ 1 + $${1 \over 2}$$ $$ \times $$ 3 + 1 $$ \times $$ 1.5
= 6.5 %
A = $${{{P^3}{Q^2}} \over {\sqrt R S}}$$
$$\therefore\,\,\,\,$$ $${{\Delta A} \over A}$$ = 3 $${{\Delta P} \over P}$$ + 2 $${{\Delta Q} \over Q}$$ + $${1 \over 2}$$ $${{\Delta R} \over R}$$ + $${{\Delta S} \over S}$$
Maximum percentage error in the value of A is
$${{\Delta A} \over A}$$ $$ \times $$ 100 = 3 $$ \times $$ 0.5 + 2 $$ \times $$ 1 + $${1 \over 2}$$ $$ \times $$ 3 + 1 $$ \times $$ 1.5
= 6.5 %
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