Question:medium

Consider the statement(s) given below :
(A). The porosity of a material is dependent upon the arrangement of the particles, shape of grains and degree of assortment.
(B). The rhombohedral arrangement gives the maximum porosity.
(C). Transmissivity is expressed as sq. metres per day.

Choose the correct answer from the options given below:

Show Hint

Remember:
- Cubic packing = Loosest \(\implies\) Max porosity (\(47.6\%\)).
- Rhombohedral packing = Tightest \(\implies\) Min porosity (\(26\%\)).
  • (B) and (C) only.
  • (A) and (C) only.
  • (A) and (B) only.
  • (C) only.
Show Solution

The Correct Option is B

Solution and Explanation

Step 1: Check statement A about what controls porosity.
Porosity of a granular medium is governed by how the grains are packed together, which depends on the shape of the individual grains, how well sorted or assorted the grain sizes are, and the resulting arrangement of the void spaces between them. This is a standard, accurate description, so statement A is true.
Step 2: Check statement B by comparing packing arrangements.
For uniform spherical grains, a cubic packing, with each grain sitting directly above the one below, leaves the largest voids and gives the maximum possible porosity of about 47.6 percent. A rhombohedral packing tilts the spheres so each nestles into the pocket formed by four neighbours, which is the tightest possible packing and gives the minimum porosity of about 26 percent. So rhombohedral arrangement actually gives minimum, not maximum, porosity, making statement B false.
Step 3: Check statement C about the unit of transmissivity.
Transmissivity is hydraulic conductivity multiplied by the saturated thickness of the aquifer, so its unit is a length rate multiplied by a length, giving an area per unit time, commonly expressed as square metres per day. This matches statement C exactly, so it is true.
Step 4: Combine the three findings.
A and C hold up while B is the reverse of the true relationship, so only A and C are correct together.
\[ \boxed{(A) and (C) only.} \]
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