Step 1: Understanding the Question:
We need to identify the laboratory test that is used to indirectly measure the tensile strength of a rock sample.
Step 2: Detailed Explanation:
Directly pulling on a rock specimen to measure its tensile strength is very difficult.
The sample is hard to grip without crushing it, and it's difficult to ensure a pure tensile failure.
Therefore, indirect methods are commonly used.
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Compressive Strength Tests (A and B): These tests measure the rock's strength under compression, not tension.
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Protodyaknov Strength Index: This is an impact test used to estimate rock strength, primarily related to its cuttability and drillability, not a standard measure of tensile strength.
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Brazilian Test (or Indirect Tensile Test): This is the standard indirect method for determining the tensile strength of rock.
In this test, a cylindrical disc of rock is placed on its side and compressed along its diameter.
This compressional loading induces a relatively uniform tensile stress across the vertical diameter of the disc.
The disc fails by splitting in tension along this diameter.
The tensile strength is then calculated from the compressional load at which failure occurs.
Step 3: Final Answer:
The indirect method for determining the tensile strength of a rock specimen is the Brazilian test.
This corresponds to option (C).