Two metalic spheres p and Q are made of same material have same smoothness but the weight of p is 8 times that of Q if the two are heated to same temperature and left to cool then the ratio of rate of cooling of Q to that of p is

Options

A. 4
B. 8
C. 2
D. 1

Answer

C

Explanation

Given weight of meterial P is 8 times the wieght of material Q
i.e., `m_(p) = 8m_(q)`
the rate of heat radiation from an object is given by
`(Delta Q) /(Delta t ) = e Sigma AT ^(4)`
Where e = emissivity `Sigma = ` Stefan. s constant
A= area and T = Temperature
But `Delta Q = mcDelta T`
From Eqs (i ) and (ii) We get
`(mcDelta T)/(Delta t) = e Sigma At^(4)`
But `m= (4)/(3) pi r^(3) Sigma `
`:. A = 4 pi r^(2) = 4pi ((3m)/( 4pi Sigma ))^((2)/(3))`
`(Delt T)/(Delta t) = (e Sigma T^(4))/( m c) [4pi ((3m )/( 4pi Sigma ))^((2)/(3)) ]`
`:. ((Delta T)/(Delta t))/((Delta T)/(Delta t)) = (m_(p))/(m_(Q))^((1)/(3)) = ((8m_(Q))/(m_(q)))^((1)/(3)) = (8)^((1)/(3)) = 2`