[Given : Mass of planet \[=8\times {{10}^{22}}kg;\] |
Radius of planet \[=2\times {{10}^{6}}m,\] |
Gravitational constant |
\[G=6.67\times {{10}^{11}}\]\[\text{ }N{{m}^{2}}/k{{g}^{2}}\]] |
A) 9
B) 11
C) 13
D) 17
Correct Answer: B
Solution :
\[{{F}_{g}}=\frac{m{{\text{v}}^{2}}}{r}\] \[\frac{\text{GMm}}{{{r}^{2}}}=\frac{m{{\text{v}}^{2}}}{r}\] \[V=\sqrt{\frac{\text{GM}}{r}}=\sqrt{\frac{(6.67\times {{10}^{-11}})(8\times {{10}^{22}})}{2.02\times {{10}^{6}}}}\] \[V=1.625\times {{10}^{3}}\] \[T=\frac{2\pi r}{V}\] \[n\times T=24\times 60\times 60\] \[n\left[ \frac{2\pi (2.02\times {{10}^{6}}}{1.625\times {{10}^{3}}} \right]=24\times 3600\] \[n=\frac{24\times 3600\times 1.625\times {{10}^{3}}}{2\pi (2.02\times {{10}^{6}})}\] \[n=11\]You need to login to perform this action.
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