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 :
Analyzing Tensile Strength Tester: Pendulum Lever Principle
This question involves evaluating two statements about the working principle of a single thread tensile strength tester.
Assertion (A) Analysis
Assertion (A) states that the single thread tensile strength tester works on the pendulum lever principle. Many tensile strength testers, particularly those used for materials like paper (e.g., Elmendorf testers), utilize a pendulum mechanism. The breaking of the specimen causes a change in the pendulum's position, which is then measured to determine the force. Therefore, this statement is correct.
Reason (R) Analysis
Reason (R) states that 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 a pendulum system designed for force measurement, the torque exerted by the pendulum is often related to the angle $\theta$ from the vertical. For instance, the restoring torque due to gravity is proportional to $\sin(\theta)$. When this torque is balanced by the force applied to break the specimen, the force measured is indeed linked to the sine of the pendulum's angular displacement. This physical relationship is fundamental to how the pendulum lever principle is applied.
Evaluating the Explanation
The pendulum lever principle relies on measuring the force indirectly through the motion of a pendulum. Reason (R) precisely describes the physical relationship between the applied force (which causes the pendulum to move) and the resulting angular displacement ($\sin(\theta)$). This explains *how* the pendulum lever principle operates in this testing apparatus.
Conclusion
Since both Assertion (A) and Reason (R) are factually correct, and Reason (R) provides the underlying physical explanation for the operation described in Assertion (A), they are both correct and (R) is the correct explanation of (A).
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