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Q.

Length of a hollow tube is 5 m, its outer diameter is 10 cm and thickness of its wall is 5 mm. If resistivity of the material of the tube is $1 .7 \times 10^{- 8} Ωm$ then resistance of tube will be

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a

$5.6 \times 10^{- 5} Ω$

b

$4 \times 10^{- 5} Ω$

c

$2 \times 10^{- 5} Ω$

d

None of these

answer is A.

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Detailed Solution

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$\begin{array}{l} By using R = ρ . \frac{l}{A}; here A = π (r_{2}^{2} - r_{1}^{2}) \\ Outer radius r_{2} = 5 cm \\ Inner radius r_{1} = 5 - 0 .5 = 4 .5 cm \end{array}$

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$\begin{array}{l} So R = 1 .7 \times 10^{- 8} \times \frac{5}{π \{{(5 \times 10^{- 2})}^{2} - {(4 .5 \times 10^{- 2})}^{2}\}} \\ = 5 .6 \times 10^{- 5} Ω \end{array}$

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Length of a hollow tube is 5 m, its outer diameter is 10 cm and thickness of its wall is 5 mm. If resistivity of the material of the tube is 1.7×10−8Ωm then resistance of tube will be