Physical quantity x and y are related as y = 4 t a n 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 .

d y d x = 4 s e c 2 x , Δ y y = 4 s e c 2 Δ x 4t a n x Δ y y × 100 = 4 s e c 2 x 4 t a n x × Δ x × 100 = 2 × Δ x × 100 Δ x x × 100 = 2 100 Δ x = 2 × π 4 = π 2 Δ y y × 100 = π 2

Physics - Error Question with Solution | TestHub

PhysicsErrorMiscellaneousEasy2 minPYQ_2020

PhysicsEasysingle choice

Physical quantity x and y are related as $y = 4 t a n x$ . If at $x = \frac{π}{4}$ radian error in measurement of $x$ is $2 %$ then find $%$ error in measurement of $y$ at $x = \frac{π}{4}$ .

Options:

Answer:

Solution:

$\frac{d y}{d x} = 4 {s e c}^{2} x, \frac{Δ y}{y} = \frac{4 {s e c}^{2} Δ x}{4t a n x}$

$\frac{Δ y}{y} \times 100 = \frac{4 {s e c}^{2} x}{4 t a n x} \times Δ x \times 100$

$= 2 \times Δ x \times 100$

$\frac{Δ x}{x} \times 100 = 2$

$100 Δ x = 2 \times \frac{π}{4} = \frac{π}{2}$

$\frac{Δ y}{y} \times 100 = \frac{π}{2}$

Stream:NTA_ABHYASSubject:PhysicsTopic:ErrorSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2020

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