Dimensions of a cone are measured using a scale with a least count of 2 mm . diameter of base and he

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1.Units, Dimensions and Measurement

easy

The dimensions of a cone are measured using a scale with a least count of $2 mm$. The diameter of the base and the height are both measured to be $20.0 cm$. The maximum percentage error in the determination of the volume is. . . . .

A

$2$

B

$3$

C

$4$

D

$5$

(IIT-2024)

Solution

$V =\frac{1}{3} \pi\left(\frac{ D }{2}\right)^2 H$

$\therefore \%$ Error in $V =2(\%$ error in $D )+\%$ error in $H$.

$\because$ Least count is $2 mm$.

$\therefore \%$ error in D $=\frac{2 mm }{20 cm } \times 100 \%=1 \%$

% error in $H =\frac{2 mm }{20 cm } \times 100 \%=1 \%$

So $\%$ error in $V =2 \times 1 \%+1 \%=3 \%$

Standard 11

Physics

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