Question

Given below are two statements one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The single thread tensile strength tester works on pendulum lever principle. Reason (R): The force acting on the specimen is directly proportional to the sine of the angle through which the pendulum is lifted from its vertical rest position. In the light of the above statements, choose the most appropriate answer from the options given below:

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

The pendulum lever principle is a classic example of "Constant Rate of Traverse" (CRT) where the load increases as the pendulum swings higher.

Answer 1

The Correct Option is A

Concept: Tensile strength testing of yarn often utilizes the Constant Rate of Traverse (CRT) principle, where a pendulum lever acts as the load-measuring mechanism.

Step 1: Analyzing Assertion (A).
Traditional single thread testers, like the stelometer or pendulum-type testers, operate on the pendulum lever principle. As the specimen is pulled, it displaces a weighted pendulum from its equilibrium. Thus, (A) is correct.

Step 2: Analyzing Reason (R).
In a pendulum system, the restoring torque is governed by the weight of the pendulum and the horizontal distance from the pivot. This distance is determined by the sine of the angle ($\theta$) of displacement. Therefore, the force or tension recorded is directly proportional to $\sin(\theta)$. Thus, (R) is correct.

Step 3: Evaluating the Relationship.
Because the trigonometric relationship described in (R) is the fundamental physics governing how the pendulum lever (A) measures force, the reason is the correct explanation for the assertion.