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Two uniform solid spheres A and B of sam...

Two uniform solid spheres `A` and `B` of same material, painted completely black and placed in free space separately. Their radii are `R` and `2R` respectively and the domainating wavelengths in their spectrum are observed to be in the ratio `1:2`, which of the following is not correct.

A

Ratio of their rates of heat loss is `4:1`

B

Ratio of their rates of cooling is `32:1`

C

Ratio of their temperatures is `2:1`

D

Ratio of their emissive powers is `4:1`

Text Solution

Verified by Experts

The correct Answer is:
D
`lamda_(1)T_(1)=lamda_(2)T_(2)`
`(T_(1))/(T_(2))=(lamda_(2))/(lamda_(1))=2`
Rate of heat loss `dotQ=4pir^(2)sigma eT^(4)`
`(dotQ_(1))/(dotQ_(2))=((r_(1))/(r_(2)))^(2)((T_(1))/(T_(2)))^(4)=4`
`dotQ=-ms(d theta)/(dt)=-4/3pir^(3) rho s(d theta)/(dt)`
`(((d theta)/(dt))_(1))/(((d theta)/(dt))_(2))=((dotQ_(1))/(dotQ_(2))).((r_(2))/(r_(1)))^(3)=32`
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