A) \[d\]
B) \[\sqrt{d}\]
C) \[1/\sqrt{d}\]
D) \[1/d\]
Correct Answer: C
Solution :
Density of the Planet can be written as \[\rho =\frac{m}{v}=\frac{m}{\frac{4}{3}\pi {{a}^{3}}}\] \[\Rightarrow \] \[\rho \propto \frac{1}{{{a}^{3}}}\] According to Keplers law, \[{{T}^{2}}\propto {{a}^{3}}\] \[\Rightarrow \] \[{{T}^{2}}\propto \frac{1}{\rho }\] Or \[T\propto \frac{1}{\sqrt{\rho }}=\frac{1}{\sqrt{d}}\] \[[\because \rho =d]\]You need to login to perform this action.
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