A steel tape is calibrated at 20- C - when the temperature of the day is -10- C - the percentage error in the measurement with the tape is - -12 - 10-6- C

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Standard XII

Mathematics

Intersection of Sets

A steel tape ...

Question

A steel tape is calibrated at $20^{\circ} C$ . when the temperature of the day is $- 10^{\circ} C$ , the percentage error in the measurement with the tape is ( $α = 12 \times 10^{- 6} /^{\circ} C$ )

3.6%

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0.36%

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0.18%

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0.036%

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Solution

The correct option is D 0.036%
We know,
$l_{2} = l_{1} (1 + α d t)$ where dt = change in temperature = $30^{0}$ C
The percentage error in the measurement will be,
(dl/l) X100 = $α$ dt 100 = $12 \times 30 \times 100 \times 10^{- 6}$
= $36 \times 10^{- 3}$ = 0.036%

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A steel tape is calibrated at 20∘C . when the temperature of the day is −10∘C , the percentage error in the measurement with the tape is (α=12×10−6/∘C)

The correct option is D 0.036%We know,l2=l1(1+αdt) where dt = change in temperature = 300 CThe percentage error in the measurement will be,(dl/l) X100 = α dt 100 =12×30×100×10−6 =36×10−3 = 0.036%

A steel tape is calibrated at $20^{\circ} C$ . when the temperature of the day is $- 10^{\circ} C$ , the percentage error in the measurement with the tape is ( $α = 12 \times 10^{- 6} /^{\circ} C$ )

The correct option is D 0.036%
We know,
$l_{2} = l_{1} (1 + α d t)$ where dt = change in temperature = $30^{0}$ C
The percentage error in the measurement will be,
(dl/l) X100 = $α$ dt 100 = $12 \times 30 \times 100 \times 10^{- 6}$
= $36 \times 10^{- 3}$ = 0.036%