Let us consider that our galaxy consists of `2.5xx10^(11)` stars each of one solar mass. How long will this star at a distance of `50,000` light year from the galastic entre take to complete one revolution? Take the diameter of the Milky way to be `10^5ly. G=6.67xx 10^(-11) Nm^(2) Kg^(-2). (1 ly= 9.46xx10^(15)m)`

Explanation

Here `M=2.5xx10^(11)` solar mass
`=2.5xx10^(11)xx(2xx10^(30))kg=5.0xx10^(41)kg`
`r=50,000ly=50,000xx9.46xx10^(15)m`
`=4.73xx10^(20)m`
We know that `M=(4pi^(2)r^(3))/(GT^(2))`
`T=((4pi^(2)r^(3))/(GM))^(1/2)=[(4xx(22//7)^(2)xx(4.73xx10^(20))^(3))/((6.67xx10^(-11))xx(5.0xx10^(41)))]^(1/2)`
`=3.53x10^(14)s`