Mathematics in Physics

JEE Main level, single correct, medium

110 of 121

Question 110 of 121

The following observations were taken for determining surface tension TT of water by capillary method:

diameter of capillary, D=1.25×10−2mD=1.25\times {10}^{-2}m

rise of water, h=1.45×10−2mh=1.45\times {10}^{-2}m

Using g=9.80ms−2g=9.80m{s}^{-2} and the simplified relation T=rhg2×103Nm−1T=\dfrac{rhg}{2}\times {10}^{3}N{m}^{-1} the possible error in surface tension is closest to:

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Answer: (C) 1.51.5%

Percentage error in surface tension

∆TT=∆rr+∆hh\dfrac{∆T}{T}=\dfrac{∆r}{r}+\dfrac{∆h}{h}

∆rr=∆DD=0.011.25\dfrac{∆r}{r}=\dfrac{∆D}{D}=\dfrac{0.01}{1.25}

∆hh=0.011.45\dfrac{∆h}{h}=\dfrac{0.01}{1.45}

∴∴%errorinT=\dfrac{∆T}{T}\times 100=\left[\dfrac{0.01}{1.25}+\dfrac{0.01}{1.45}\right]\times 100=1.489\approx 1.5

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