A) \[6\times {{10}^{41}}\]
B) \[5\times {{10}^{41}}\]
C) \[4\times {{10}^{41}}\]
D) \[3\times {{10}^{41}}\]
E) \[2\times {{10}^{41}}\]
Correct Answer: D
Solution :
Mass of galaxy is given by \[M=\frac{{{v}^{2}}r}{G}\] Given, \[v=250\text{ }km/s=250\times {{10}^{3}}m/s\] \[r=3\times {{10}^{4}}\]light year\[=3\times {{10}^{4}}\times {{10}^{16}}\] \[\approx 3\times {{10}^{20}}m.\] \[\therefore \] \[M=\frac{(250\times {{10}^{3}})\times 3\times {{10}^{20}}}{6.6\times {{10}^{-11}}}=3\times {{10}^{41}}kg\]
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