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  4. Two stars A and B at equal surface temperature. Star A has surface area four times that of B. The ratio in the luminosities of A and B will be

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Q. Two stars A and B at equal surface temperature. Star A has surface area four times that of B. The ratio in the luminosities of A and B will be

AMUAMU 1998

Solution:

: Luminosity of a star $ L=\sigma 4\pi {{R}^{2}}{{T}^{4}} $ $ \therefore $ $ \frac{{{L}_{A}}}{{{L}_{B}}}=\frac{Surface\text{ }area\text{ }of\text{ }star\text{ }A}{Surface\text{ }area\text{ }of\text{ }star\text{ }B} $ $ \therefore $ $ \frac{{{L}_{A}}}{{{L}_{B}}}=\frac{4}{1} $