A) \[{{R}^{2}}\sqrt{4\pi G\rho /3}\]
B) \[R\sqrt{4\pi G\rho /3}\]
C) \[{{R}^{2}}\sqrt{8\pi G\rho /3}\]
D) \[R\sqrt{8\pi G\rho /3}\]
Correct Answer: D
Solution :
Escape velocity \[v=\sqrt{\frac{2GM}{R}}\] \[=\sqrt{\frac{2G\times \frac{4}{3}\pi {{R}^{3}}\rho }{R}}=R\sqrt{\frac{8}{3}\pi G\rho }\]
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