The diameter and height of a cylinder are measured by a meter scale to be 12.6 ± 0.1 c m and 34.2 ± 0.1 c m , respectively. What will be the value of its volume in appropriate significant figures?

V = π d 2 h 4 = π 4 12.6 2 34.2 c m 3 d V V = 2 d d d + d h h Converting to errors ∆ V V = 2 ∆ d d + ∆ h h ∆ V 4260 = 2 0.1 12.6 + 0.1 34.2 ⇒ ∆ V = 80 c m 3 V = 4260 ± 80 c m 3

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Physics - Error Question with Solution | TestHub

PhysicsErrorMiscellaneousEasy2 minPYQ_2019

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The diameter and height of a cylinder are measured by a meter scale to be $12.6 \pm 0.1 c m$ and $34.2 \pm 0.1 c m$ , respectively. What will be the value of its volume in appropriate significant figures?

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Answer:

Solution:

$V = \frac{π d^{2} h}{4} = \frac{π}{4} {(12.6)}^{2} (34.2) c m^{3}$

$\frac{d V}{V} = \frac{2 d (d)}{d} + \frac{d (h)}{h}$

Converting to errors

$\frac{∆ V}{V} = 2 \frac{∆ d}{d} + \frac{∆ h}{h}$

$\frac{∆ V}{4260} = 2 (\frac{0.1}{12.6}) + (\frac{0.1}{34.2})$

$\Rightarrow ∆ V = 80 c m^{3}$

$V = 4260 \pm 80 c m^{3}$

Stream:JEESubject:PhysicsTopic:ErrorSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2019

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