Question

In astronomy order of magnitude estimation plays an important role. The derivative `(dp)/(dt)` can be taken difference ration `(DeltaP)/(Deltar)`. Consider the star has a radius `R`, pressure at its centre is `P_(e)` and pressure at outer layer is zero is the average mass is `(M_(Q))/2` and average radius `(R_(o))/2` then the expression for `P_(c)` is
A. `P_(c)=3/2(GM_(0)^(2))/(piR_(0)^(4))`
B. `P_(c)=2/(3pi)(GM_(0)^(2))/(R_(0)^(4))`
C. `P_(c)=2/3(GM_(0)^(2))/(piR_(0)^(4))`
D. `P_(c)=3/2(GM_(0)^(2))/(R_(0)^(4))`

Answer 1

Correct Answer - A
The net force acting on the system is
`|vec(F)_(1)+vec(F)_(2)|=0`
`rArr ` the linear momentum of the system is conserved
`rArr m_(A)v_(A)=m_(B)v_(B)`
`rArr v_(A)=(m_(B))/(m_(A))v_(B)=2/1xx3.6=7.2cm//hr`
`=(7.2xx10^(-2))/(3.6xx10^(3))=(7.2xx10^(-2))/3600=(7.2xx10^(-2))/(3.6xx10^(3))=2xx10^(-5)`
In `10^(-5)m//s, v_(A)=2`