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Q.

Consider a white dwarf and of solar mass. The radius of the white dwarf is same as that of the earth. Determine the density of the white dwarf star. [Mass of sun= $2 \times 10^{30} k g;$ Radius of earth $= 6400 k m$ ]

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a

$1.822 \times 10^{9} k g / m^{3}$

b

$1.628 \times 10^{9} k g / m^{3}$

c

$1.648 \times 10^{9} k g / m^{3}$

d

$1.422 \times 10^{9} k g / m^{3}$

answer is A.

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Detailed Solution

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$D e n s i t y = \frac{M a s s}{v o l u m e} = \frac{M}{\frac{4}{3} π r^{3}} M = M_{S u n} = M_{W h i t e d w a r f} = 2 \times 10^{30} k g; r a d i u s r = 6400 \times 10^{3} m . = \frac{2 \times 10^{30} \times 3}{4 \times 3.14 \times {(64 \times 10^{5})}^{3}} = 1.822 \times 10^{9} k g / m^{3} D e n s i t y o f w h i t e d w a r f = 1.822 \times 10^{9} k g / m^{3} .$

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