Q

# Help me answer: - Physics and Measurement - JEE Main

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 $A= \frac{p^{3}Q^{2}}{\sqrt{R}S}$

The maximum percentage error in the value of A will be :

• Option 1)

6.0%

• Option 2)

7.5%

• Option 3)

8.5%

• Option 4)

6.5%

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N

As we have learned

Error in quantity raised to some power -

$\dpi{100} x=\frac{a^{n}}{b^{m}}\rightarrow \frac{\Delta x}{x}=\pm \left ( n\frac{\Delta a}{a}+m\frac{\Delta b}{b} \right )$

- wherein

$\dpi{100} \Delta a$= absolute error in measurement of a

$\dpi{100} \Delta b$= absolute error in measurement of b

$\dpi{100} \Delta x$= absolute error in measurement of x

$\frac{\Delta P }{P} 100 \%= 0.5$     $\frac{\Delta Q}{Q}\times 100\%= 1$

$\frac{\Delta R}{R}\times 100\%= 3$   $\frac{\Delta S}{S}\times 100\% =1.5$

$\frac{\Delta A}{A}\times 100\% =3\frac{\Delta P}{P}\times 100\%+2\frac{\Delta Q}{Q}\times 100\%+1/2 \frac{\Delta R}{R}\times 100\%+\frac{\Delta S}{S}\times 100\%$

$3\times 0.5+2\times 1+1/2\times 3+1.5=6.5 \%$

Option 1)

6.0%

This is incorrect

Option 2)

7.5%

This is incorrect

Option 3)

8.5%

This is incorrect

Option 4)

6.5%

This is correct

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