A hollow copper sphere & a hollow copper cube of same surface area & negligible thickness , are filled with warm water of same temperature and placed

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A hollow copper sphere & a hollow copper cube of same surface area & negligible thickness , are filled with warm water of same temperature and placed in an enclosure of constant temperature a few degrees below that of the bodies. Then in the beginning:-
A. The rate of energy lost by the sphere is greater than that by the cube
B. The rate of energy lost by the two are equal
C. The rate of energy lost by the sphere is less than that by the cube
D. The rate of fall of temperature for sphere is less than that for the cube


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Salim Ahmed Kawsar

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Correct Answer - B::D
For surface areas to be same
`S_("sphere") = S_("cube") implies 4piR^(2) = 6a^(2) implies (a)/(R) = sqrt((2pi)/(3)) (gt1`)
Volume ratio
` (V_("sphere"))/(V_("cube")) = ((4)/(3)piR^(3))/(a^(3)) = (2R)/(a) = sqrt((6)/(pi)) (gt1`)
`therefore` (Mass of water in sphere)`gt` (Mass of water in cube)

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