JEE Advanced2015PhysicsMechanical Properties of FluidsActual
A spherical body of radius R consists of a fluid of constant density and is in equilibrium under its own gravity. If P ( r ) is the pressure at r ( r < R ) , then the correct option(s) is (are)
Options
- AP r = 0 = 0
- BP r = 3 R 4 P r = 2 R 3 = 63 80
- CP r = 3 R 5 P r = 2 R 5 = 16 21
- DP r = R 2 P r = R 3 = 20 27
Correct answer
B. P r = 3 R 4 P r = 2 R 3 = 63 80
Step-by-step solution
d E = P - P + d P A ⇒ G m r 2 d m = - d P A ⇒ ∫ 0 P d P = - ∫ E r G M r 3 R 3 4 a r 2 d r ρ r 2 4 π r 2 ∴ P = G ρ M 2 R 1 - r 2 R 2