GATE ME 2021 Set 1 — Question 41
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Strength of Materials → Stress, Strain & Elastic Constants → Stress & Strain
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Question
A right solid circular cone standing on its base on a horizontal surface is of height and base radius . The cone is made of a material with specific weight and elastic modulus . The vertical deflection at the mid-height of the cone due to self-weight is given by
Correct answer
(A) (wH²)/(8E)
Solution
Let be the distance from the apex of the cone. The weight of the portion of the cone above is , where . The cross-sectional area at is . The stress due to self-weight at distance from apex is . The deflection of a point at distance from the apex is given by . For mid-height, . Thus, .
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