Question

The sun revolves around galaxy with speed of $250km/s$ around the center of milky way and its radius is $3\times {10}^4$ light year. The mass of milky way in $kg$ is

• A. $6\times {10}^{41}$
• B. $5\times {10}^{41}$
• C. $4\times {10}^{41}$
• D. $3\times {10}^{41}$

Answer 1

The correct option is D $3\times {10}^{41}$

Let mass of sun $=m$ and mass of galaxy $=M$

So, $\frac{GMm}{r^2}=\frac{m{v}^2}{r}$

or, $M=\frac{v^{2}r}{G}=\frac{(250\times {10}^3{)}^2\times 3\times {10}^4\times 9.461\times {10}^{15}}{6.67\times {10}^{-11}}=2.66\times {10}^{41}\approx 3\times {10}^{41}$