A physical quantity y is represented by the formula y = m ^ 2 r ^ - 4 g ^ x l ^ - (3)/(2) If the percentage errors found in y, m, r, l and g are 18, 1, 0 . 5, 4 and p respectively, then find the value of x and p .

Correct answer: C. (16)/(3) and ± (3)/(2) ( )/(y) = (2 )/(m) + (4 )/(r) + (x )/(g) + (3)/(2)( )/(l) 18 = 2 ( 1 ) + 4 ( 0 . 5 ) + xp + (3)/(2) ( 4 ) 8 = xp By checking from options. x = (16)/(3), p = ± (3)/(2)

JEE Main 202127 JulyEvening Shift

Exam: JEE Main
Year: 2021
Date: 27 July
Shift: Evening Shift
Subject: Physics
Chapter: Mathematics in Physics

JEE Main 2021 · 27 July · Evening Shift · Physics · Mathematics in Physics

A physical quantity y is represented by the formula y = m ^ 2 r ^ -...

A physical quantity

y

is represented by the formula

y = {m}^{2}{r}^{- 4}{g}^{x}{l}^{- \dfrac{3}{2}}

If the percentage errors found in

y, m, r, l

and

g

are

18, 1, 0 . 5, 4

and

p

respectively, then find the value of

x

and

p

Options

A $5$ and $\pm 2$
B $4$ and $\pm 3$
C $\dfrac{16}{3}$ and $\pm \dfrac{3}{2}$
D $8$ and $\pm 2$

Correct answer

C. $\dfrac{16}{3}$ and $\pm \dfrac{3}{2}$

Step-by-step solution

$\dfrac{\Deltay}{y} = \dfrac{2\Deltam}{m} + \dfrac{4\Deltar}{r} + \dfrac{x\Deltag}{g} + \dfrac{3}{2}\dfrac{\Deltal}{l}$

$18 = 2 ( 1 ) + 4 ( 0 . 5 ) + xp + \dfrac{3}{2} ( 4 )$

$8 = xp$

By checking from options.

$x = \dfrac{16}{3}, p = \pm \dfrac{3}{2}$

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