Physical quantity x and y are related as y = 4 x . If at x = (π)/(4) radian error in measurement of x is 2% then find % error in measurement of y at x = (π)/(4) .

Correct answer: B. (π)/(2)% (dy)/(dx) = 4 ^ 2 x, ( )/(y) = 4 ^ 2 4 x ( )/(y) × 100 = 4 ^ 2 x 4 x × × 100 = 2 × × 100 ( )/(x) × 100 = 2 100 = 2 × (π)/(4) = (π)/(2) ( )/(y) × 100 = (π)/(2)

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Physics
Chapter: Units and Dimensions

NTA Abhyas 2020 · Physics · Units and Dimensions

Physical quantity x and y are related as y = 4 x . If at x =...

Physical quantity x and y are related as

y = 4\tan x

. If at

x = \dfrac{\pi}{4}

radian error in measurement of

x

2%

then find

%

error in measurement of

y

x = \dfrac{π}{4}

Options

A $2%$
B $\dfrac{\pi}{2}%$
C $\dfrac{\pi}{6}%$
D $\pi%$

Correct answer

B. $\dfrac{\pi}{2}%$

Step-by-step solution

\dfrac{dy}{dx} = 4\sec^{2}x, \dfrac{\Deltay}{y} = \dfrac{4\sec^{2}\Deltax}{4\tan x}

\dfrac{\Deltay}{y} \times 100 = \dfrac{4\sec^{2}x}{4\tan x} \times \Deltax \times 100

= 2 \times \Deltax \times 100

\dfrac{\Deltax}{x} \times 100 = 2

100\Deltax = 2 \times \dfrac{\pi}{4} = \dfrac{\pi}{2}

\dfrac{\Deltay}{y} \times 100 = \dfrac{\pi}{2}

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