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Spheres P and Q are uniformally construc...

Spheres `P` and `Q` are uniformally constructed from the same material which is 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 temperture. Find the value of `'x'` :

A

`1//4`

B

`1//3`

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
C
`((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`
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