A) \[36\,\,{{v}_{es}}\]
B) \[12\,{{v}_{es}}\]
C) \[6\,\,{{v}_{es}}\]
D) \[20\,\,{{v}_{es}}\]
Correct Answer: B
Solution :
The escape velocity for the surface of earth is \[{{V}_{se(e)}}\,\,=\,\,\sqrt{\frac{2G{{M}_{e}}}{{{\operatorname{R}}_{e}}}}\] \[or\,\,{{v}_{es(e)}}\,=\,\,{{\operatorname{R}}_{e}}\,\sqrt{\frac{8}{3}}\,G\pi \rho \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[ \because \,\,{{M}_{e}}=\frac{4}{3}\,\pi {{R}^{3}} \right]\]\[=\,\,{{\operatorname{R}}_{e}}\,\sqrt{\frac{8}{3}G\pi \rho }\] \[Hence,\,\,\frac{{{v}_{es(e)}}}{{{v}_{es(P)}}}\,\,=\,\,\frac{{{\operatorname{R}}_{e}}\sqrt{\frac{8}{3}G\pi \rho }}{4{{\operatorname{R}}_{e}}\sqrt{\frac{8}{3}G\pi 9\rho }}\,\,=\,\,\frac{1}{12}\] \[So,\,\,{{v}_{e}}{{_{s}}_{\left( p \right)}}\,\,=\,\,12\,{{v}_{es\left( e \right)}}\]
You need to login to perform this action.
You will be redirected in
3 sec
