The mass density of a spherical body is given by ρ(r)=kr for r≤R and ρ(r)=0 for r>R, where r is the distance from the centre. The correct graph that describes qualitatively the acceleration, a, of a test particle as a function of r is :<p></p>

Mass density ρ(r)=kr r≤R
Charge inside of r radius sphere= ∫r 0 krdr ×4πr² ⇒charge =4kπ[r²/2] ⇒charge =4kπr²/2 ⇒∫E.dA=Q/ε₀ ⇒E=Q/4πε₀ ×r² ⇒E=2Kπr²/4πε₀ ×r² ⇒[E=K/2ε₀],r≤R
If,r≥R ⇒E=KQ/r²,[Q=2KπR²]
Hence, the plot is given here.

Eduprobe

Question:

The mass density of a spherical body is given by ρ(r)=kr for r≤R and ρ(r)=0 for r>R, where r is the distance from the centre. The correct graph that describes qualitatively the acceleration, a, of a test particle as a function of r is :

Solution: