Black holes are objects whose gravitational field is so

strong that not even light can escape. One way of thinking about

this is to consider a spherical object whose density is so large that

the escape speed at its surface is greater than the speed of light, c$.$ If

a star$$s radius is smaller than a value called the Schwarzschild radius

then the star will be a black hole, that is$,$ light originating from

its surface cannot escape. $($a$)$ For a nonrotating black hole, the

Schwarzschild radius depends only upon the mass of the black

hole. Show that it is related to that mass M by

$($b$)$ Calculate the value of the Schwarzschild radius for a black hole

whose mass is ten solar masses.