JEE Advanced2017PhysicsUnits and DimensionsActual
Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the instantaneous density ρ remains uniform throughout the volume. The rate of fractional change in density 1 ρ d ρ d t is constant. The velocity v of any point on the surface of the expanding sphere is proportional to
Options
- AR 3
- B1 R
- CR
- DR 2 3
Correct answer
C. R
Step-by-step solution
Density of sphere is ρ = m v = 3 m 4 π R 3 ⇒ 1 ρ d ρ d t = - 3 R d R d t Since ⇒ 1 ρ d ρ d t is constant ∴ d R d t ∝ R