Q1: Sphericity of a cubical particle, when its equivalent diameter is taken as the height of the cube, is

ANS:B - 1

The sphericity of a cubical particle, when its equivalent diameter is taken as the height of the cube, is 0.5.

Explanation:

• Sphericity: Sphericity is a measure of how closely the shape of a particle approaches that of a sphere. It is defined as the ratio of the surface area of a sphere with the same volume as the particle to the surface area of the particle itself.
• For a Cubical Particle:
  • If the equivalent diameter DDD of a cubical particle is taken as the height of the cube, then the volume VVV of the cube can be calculated as V=D3V = D^3V=D3.
  • The surface area AAA of the cube is A=6D2A = 6D^2A=6D2.
  • The volume of a sphere with the same diameter DDD is Vsphere=π6D3V_{\text{sphere}} = \frac{\pi}{6} D^3Vsphere​=6π​D3.
  • The surface area of the sphere is Asphere=πD2A_{\text{sphere}} = \pi D^2Asphere​=πD2.
• Sphericity Formula: The sphericity Φ\PhiΦ is given by: Φ=π1/3D61/2\Phi = \frac{\pi^{1/3} D}{6^{1/2}}Φ=61/2π1/3D​
• Calculation for a Cubical Particle:
  • If DDD (height of the cube) is taken as the equivalent diameter, then:
  Φ=π1/3D61/2\Phi = \frac{\pi^{1/3} D}{6^{1/2}}Φ=61/2π1/3D​ For a cubical particle where DDD is the height of the cube, the sphericity Φ\PhiΦ simplifies to 12\frac{1}{2}21​.