A star can be considered as spherical ball of hot gas of radius `R`. Inside the star, the density of the gas is `rho_(r)` at radius `r` and mass of the gas within this region is `M_(r)`.
The correct differential equation for variation of mass with respect to radius is (refer to the adjacent figure)

Options

A. `(dM_(1))/(dr)=A/3pirho_(r)r^(3)`
B. `(dM_(r))/(dr)=4pirho_(r)r^(2)`
C. `(dM_(r))/(dr)=2/3pirho_(r)r^(2)`
D. `(dM_(r))/(dr)=1/3pirho_(r)r^(2)`

Answer

B

Explanation

`dM_(r)=rho_(r)pir^(2)dr`
`(dM_(1))/(dr)=rho_(r)4pir^(2)`