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Two spheres of different materials one with double the radius and one-fourth wall thickness of the other are filled with ice. If the time taken for complete melting of ice in the larger sphere is `25` minutes and for smaller one is `16` minutes, the ratio of thermal conductivities of the materials of larger sphere to that of smaller sphere is:A. `4:5`B. `5:4`C. `25:8`D. `8:25` |
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Answer» Correct Answer - 4 `H=Q/t=(KA)/(l)(theta_(1)-theta_(2))` `=(mL)/(t)=(K4piR^(2))/(l)(theta_(1)-theta_(2))` `(VrhoL)/(t)=(K4piR^(2))/(l)(theta_(1)-theta_(2))` `(4)/(3)(pir^(3)rhoL)/(t)=(K4pir^(2))/(l) (theta_(1)-theta_(2))K propto (rl)/(t)` `(K_(1))/(K_(2))=(r_(1))/(r_(2)).(l_(1))/(l_(2))xx(t_(2))/(t_(1))` `(K_(1))/(K_(2))=(2r)/(r).(l)/(4l).(16)/(25)=(8)/(25)` |
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