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Which of the following circular rods (given radius `r` and length `l`) each made of the same material and whose ends are maintained at the same temperature will conduct most heat?A. `r = 2r_(0), l = 2l_(0)`B. `r = 2r_(0), l = l_(0)`C. `r = r_(0), l = l_(0)`D. `r = r_(0), l = 2l_(0)` |
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Answer» Correct Answer - B Heat conduction through a rod is `H = (Delta Q)/(Deltat) = KA ((T_1-T_(2))/(l))` `rArr H prop (r^(2))/(l)` ..(i) When `r = 2r_(0), l = 2l_(0)` `H prop ((2r_(0))^(2))/(2l_(0)) rArr H prop (2r_(0)^(2))/(l_0)` (b) when `r = 2r_(0), l = l_(0)` `H prop ((2r_(0))^(2))/(l_(0)) rArr H prop (4r_(0)^(2))/(l_0)` (c) When `r = r_(0), l = l_(0)` `H prop ((r_(0))^(2))/(l_(0))` (d) When `r = r_(0), l = 2l_(0)` `H prop ((r_(0))^(2))/(2l_(0))` It is obvisous heat conduction will be more in case (b) |
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