A) \[{{v}_{es}}={{R}_{e}}\sqrt{\frac{8\pi }{3}\text{G }\!\!\rho\!\!\text{ }}\]
B) \[{{v}_{es}}=M\sqrt{\frac{8\pi }{3}\text{G}{{\text{R}}_{e}}}\]
C) \[{{v}_{es}}=\sqrt{2GM{{R}_{e}}}\]
D) \[{{v}_{es}}=\sqrt{\frac{2GM}{R_{e}^{2}}}\]
Correct Answer: A
Solution :
Escape velocity \[{{v}_{es}}=\sqrt{2g{{R}_{e}}}\] \[=\sqrt{2\frac{G{{M}_{e}}}{R_{e}^{2}}\times {{R}_{e}}}\] \[\left[ g=\frac{G{{M}_{e}}}{R_{e}^{2}} \right]\] \[=\sqrt{2\frac{G{{M}_{e}}}{{{R}_{e}}}}\][mass = volume \[\times \] density] \[=\sqrt{\frac{2G}{{{R}_{e}}}V\rho }\] \[=\sqrt{\frac{2G\times \frac{4}{3}\pi R_{e}^{3}\rho }{{{R}_{e}}}}=\sqrt{\frac{8}{3}\pi GR_{e}^{2}\rho }={{R}_{e}}\sqrt{\frac{8\pi }{3}G\rho }\]
You need to login to perform this action.
You will be redirected in
3 sec
