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Two spheres of radii in the ratio 1 : 2 ...

Two spheres of radii in the ratio `1 : 2` and densities in the ratio `2 : 1` and of same specific heat, are heated to same temperature and left in the same surronding. There are of cooling will be in the ratio

A

`2:1`

B

`1:1`

C

`1:2`

D

`1:4`

Text Solution

Verified by Experts

The correct Answer is:
B
Rate of cooling = `(mC Delta T)/(t)`
Mass = volume `xx` density
`=4/3 pi r^3 xx rho`
Mass per unit area =`(4/3 pi r^3 xx rho )/(4 pi r^2)=1/3 r rho`
Rate of cooling `prop` r `rho`
Ratio of cooling for two spheres - `=(r_1 rho_1)/(r_2 rho_2)=(1xx2)/(2xx1)=1:1`
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