A solid cube and a solid sphere of the same material have equal surface area. Both are at the same temperature `120^(@)C`, then

Options

A. both the cube and the sphere cool down at the same rate
B. the cube cools down faster than the sphere
C. the sphere cools down faster than the cube
D. whichever is having more mass will cool down cube

Answer

B

Explanation

(2) Rate of cooling `(dT)/(dt) = (e sigma A)/(ms) (T^(4) - T_(0)^(4))`
`(dT)/(dt) prop (1)/(m)`
Let a : edge of cube, r : radius of sphere
`6 a^(2) = 4 pi r^(2) implies r = sqrt((3)/(2 pi)) a`
`m_(cube) = m_(1) = rho . A^(3)`
`m_(sphere) = m_(2) = rho . (4)/(3) pi r^(2)`
`((dT // dt)_(cube))/((dT // dt)_(sphere)) = (m_(2))/(m_(1)) = (rho . (4)/(3) pi r^(3))/(rho . a^(3)) = (4 pi)/(3) (sqrt((3)/(2 pi)))^(3)`
`= (4 pi)/(3). (3)/(2 pi) sqrt((3)/(2 pi)) = sqrt((12)/(2 pi)) = sqrt((6)/(pi)) gt 1`