A cube and a sphere (both solid) of same mass, same material are heated upto same temperature and then kept in same surrounding. Rate of cooling means rate of fall of temperature

Options

A. Sphere will cool down at a faster rate.
B. cube will cool down at a faster rate.
C. ratio of rate of cooling of cube to sphere `=2[3/(4pi)]^(1//3)`
D. ratio of rate of cooling of cube to sphere =`1/2 (3/(4pi))^(1//3)`

Answer

BC

Explanation

`(dT)/(dt)=(CA)/(ms)(T-T_(0))`
`l^(3) P=4/3 pi R^(3) P`
`R=sqrt(3/(4pi))l`
`(dT_(C)//dt)/(dT_(s)//dt)=(A_(C))/(A_(S))=(6l^(2))/(4piR^(2))`
`=(6l^(2))/(4pixx(3//4pi)^(2//3) l^(2))=2sqrt(3/(4pi))`