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

Step-by-step solution

For Inside point r ≤ R g = E = G r 2 ∫ 0 r 4 π r 2 d r K r = G K r 2 × 4 π r 2 2 = 2 π G K = constant For outside point r > R E = g E = G M r 2 E = G r 2 ∫ 0 R ( 4 π r 2 d r ' ) ( K r ' ) E = 4 π K G r 2 [ r ' 2 2 ] 0 R E = 2 π K G r 2 R 2 E ∝ 1 r 2 .