A) \[4.3\times {{10}^{-2}}N{{m}^{-1}}\]
B) \[5.6\times {{10}^{-2}}N{{m}^{-1}}\]
C) \[6.3\times {{10}^{-2}}N{{m}^{-1}}\]
D) \[7.3\times {{10}^{-2}}N{{m}^{-1}}\]
Correct Answer: C
Solution :
Key Idea Surface tension of liquid by capillary rise is given by \[T=\frac{rhDg}{2}\]where, r is radius of capillary, D is density of liquid, h is height of liquid and g is acceleration due to gravity. Here, D = 800 kg \[{{m}^{-3}}\] G = 9.8m/\[m/{{s}^{2}}\] r = 0.4 mm \[=4\times {{10}^{-4}}m\] h = 4 cm = 0.04 m \[\left( \begin{align} & d=0.8\,mm \\ & r=\frac{d}{2} \\ \end{align} \right)\] By using the formula \[T=\frac{4\times {{10}^{-4}}\times 0.04\times 800\times 9.8}{2}\] \[=4\times {{10}^{-4}}\times 0.04\times 400\times 9.8\] \[=4\times 4\times 4\times 98\times {{10}^{-5}}\] \[=6272\times {{10}^{-5}}\] \[=6.3\times {{10}^{-2}}N{{m}^{-1}}\]
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