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Two thin metallic spherical shells of radii \( r_{1} \) and \( r_{2}\left(r_{1}<r_{2}\right) \) are placed with their…

Q1

Two thin metallic spherical shells of radii \( r_{1} \) and \( r_{2}\left(r_{1}<r_{2}\right) \) are placed with their centres coinciding. A material of thermal conductivity \( K \) is filled in the space between the shells. The inner shell is maintained at temperature \( \theta_{1} \) and the outer shell at temperature \( \theta_{2}\left(\theta_{1}<\theta_{2}\right) \). The rate at which heat flows radially through the material is

[JEE Main 2021, 31 Aug (Shift 2)]

a

\( \frac{K\left(\theta_{2}-\theta_{1}\right)}{r_{2}-r_{1}} \)

b

\( \frac{K\left(\theta_{2}-\theta_{1}\right)\left(r_{2}-r_{1}\right)}{4 \pi r_{1} r_{2}} \)

c

\( \frac{4 \pi K r_{1} r_{2}\left(\theta_{2}-\theta_{1}\right)}{r_{2}-r_{1}} \)

d

\( \frac{\pi r_{1} r_{2}\left(\theta_{2}-\theta_{1}\right)}{r_{2}-r_{1}} \)

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