SATHEE: Physics And Measurement Question 294

Physics And Measurement Question 294

Question: You measure two quantities as $A = 1.0 m \pm 0.2 m$

$B = 2.0 m \pm 0.2 m$ . We should report correct value for $\sqrt{A B}$ as

Options:

A) $1.4 m \pm 0.4 m$

B) $1.41 m \pm 0.15 m$

C) $1.4 m \pm 0.3 m$

D) $1.4 m \pm 0.2 m$

Show Answer

Answer:

Correct Answer: D

Solution:

[d] As given that, $A = 1.0 m \pm 0.2 m, B = 2.0 m \pm 0.2 m$

So, $X = \sqrt{A B} = \sqrt{(1.0) (2.0)} = 1.414 m$

Rounding off upto two significant digit $X = 1.4 m = (r) (L e t)$

$\frac{Δ x}{x} = \frac{1}{2} [\frac{Δ A}{A} + \frac{Δ B}{B}] = \frac{1}{2} [\frac{0.2}{1.0} + \frac{0.2}{2.0}] = 0.212$

Rounding off upto one significant digit $Δ x = 0.2 m = Δ r (L e t)$

So, correct value of $\sqrt{A B} = r + Δ r = (1.4 \pm 0.2) m$

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Physics And Measurement Question 294

Question: You measure two quantities as A=1.0m±0.2m

Options:

Answer:

Solution:

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Question: You measure two quantities as $A = 1.0 m \pm 0.2 m$