The length of a cylinder is measured with a meter rod having leas… - Vidyadip

MCQ

The length of a cylinder is measured with a meter rod having least count $0.1\, cm$. Its diameter is measured with vernier calipers having least count $0.01\, cm$. Given that length is $5.0 \,cm$. and radius is $2.0 \,cm$. The percentage error in the calculated value of the volume will be ......... $\%$

A
$1$
B
$2$
✓
$3$
D
$4$

✓

Answer

Correct option: C.

$3$

c
(c) Volume of cylinder $V = \pi {r^2}l$

Percentage error in volume

$\frac{{\Delta V}}{V} \times 100 = \frac{{2\Delta r}}{r} \times 100 + \frac{{\Delta l}}{l} \times 100$

$ = \left( {2 \times \frac{{0.01}}{{2.0}} \times 100 + \frac{{0.1}}{{5.0}} \times 100} \right)$

$ = (1 + 2)\% $ =$3\% $

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