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Assertion : A hollow shaft is found to...

Assertion : A hollow shaft is found to be stronger than a solid shaft made of same material.
Reason : The torque required to produce a given twist in hollow cylinder is greater than that required to twist a solid cylinder of same size and material.

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To analyze the assertion and reason provided, we will break down the statements step by step. ### Step-by-Step Solution: 1. **Understanding the Assertion**: - The assertion states that "A hollow shaft is found to be stronger than a solid shaft made of the same material." - To understand this, we need to consider the distribution of material in both shafts. A hollow shaft has material distributed away from the center, which can enhance its strength under torsional loads. 2. **Understanding the Reason**: - The reason states, "The torque required to produce a given twist in a hollow cylinder is greater than that required to twist a solid cylinder of the same size and material." - Torque (τ) is defined as τ = r × F, where r is the radius and F is the force applied. For a hollow cylinder, the effective radius where the material resists twisting is greater than that of a solid cylinder, which means that for the same material and dimensions, the hollow cylinder can withstand more torque before failing. 3. **Comparing the Strength**: - When comparing the strength of both shafts, we can analyze their polar moment of inertia (J). The polar moment of inertia for a hollow shaft is greater than that of a solid shaft for the same outer diameter, which contributes to its ability to resist twisting. - Therefore, under the same loading conditions, the hollow shaft can carry more load before yielding, making it stronger. 4. **Conclusion**: - Both the assertion and the reason are correct. The hollow shaft is indeed stronger than a solid shaft made of the same material, and the reason provided accurately explains why the torque required to twist a hollow cylinder is greater than that for a solid cylinder of the same size and material. ### Final Statement: - **Assertion**: True - **Reason**: True - Both statements are correct, and the reason correctly explains the assertion.
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