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

  1. A. 3\rho/4
  2. B. 9\rho/16 ✓
  3. C. 7\rho/8
  4. D. 5\rho/8

Correct Answer: B. 9\rho/16

Explanation

Mass of inner sphere = \rho \times \frac{4}{3}\pi (R/2)^3. Mass of shell = \frac{\rho}{2} \times [\frac{4}{3}\pi R^3 - \frac{4}{3}\pi (R/2)^3]. Total mass divided by total volume \frac{4}{3}\pi R^3 gives an average density of 9\rho/16.

Related questions on Physics

Practice more NDA GAT questions