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NDA 1 2024 GAT, question 56

Topic: Physics

Q56

A spherical shell of outer radius RR and inner radius R/2R/2 contains a solid sphere of radius R/2R/2 (see figure). The density of the material of the solid sphere is ρ\rho and that of the shell is ρ/2\rho/2. What is the average mass density of the larger sphere thus formed ?

Figure for Q56

  1. (a) 3ρ/43\rho/4
  2. (b) 9ρ/169\rho/16Correct answer
  3. (c) 7ρ/87\rho/8
  4. (d) 5ρ/85\rho/8

Solution.

Answer: (b) 9ρ/169\rho/16

  1. The inner sphere occupies (1/2)³ = 1/8 of the total volume; the shell occupies 7/8.
  2. Divide total mass by total volume: average density = ρ/8 + (ρ/2)(7/8) = 9ρ/16.