Spheres P and Q are uniformaly constructed from the same material which is a good conductor of heat and the radius of Q is thrice the radius of P. The rate of fall of temperature of P is x times that of Q when both are at the same surface temperature. The value of x is

Options

A. `1//4`
B. `1//3`
C. 3
D. 4

Answer

C

Explanation

`((dQ)/(dt))=-esigmaA_(p)T^(4),((dQ)/(dt))_(Q)=-esigmaA_(Q)T^(4)`
`(-mp^(S)((d theta)/(dt))_(p))/(-m_(Q)S((d theta)/(dt))_(Q))=(A_(p))/(A_(Q)),(V_(p))/(V_(Q))X=(4pi(r)^(2))/(4pi(3r)^(2))`
`(X)/(27)=(1)/(9),xx=3`