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Differential Calculus> The strength of a beam varies as the prod...

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The strength of a beam varies as the product of its breadth and square of its depth.Find the dimensions of the strongest beam which can be cut from a circular log of radius a.

taniska , 11 Years ago

Grade 12

1 Answers

Arun Kumar

Last Activity: 11 Years ago

Hi

$\\s=d^2*b \\$height is constant and $=h \\$lets say diagonal makes and angle $\theta$ with the breadth and radius$ \\=>b=asin\theta,d=acos\theta \\=>s=a^3*cos^2\theta sin\theta \\ {ds \over dt}=a^3*(cos^3\theta - 2cos\theta *sin^2\theta )=0 \\=>cos\theta (cos^2\theta - 2sin^2\theta)=0 \\=>cos\theta \neq 0 =>cot^2\theta =2$

Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty

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