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Q.

Maximum tensile stress that a material can withstand is $σ$ . A rod of mass m having uniform cross sectional area, made of the above mentioned material is freely suspended from one end. Then find its minimum diameter.

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a

$\sqrt{\frac{2 mg}{π σ}}$

b

$4 \sqrt{\frac{mg}{π σ}}$

c

$\sqrt{\frac{4 mg}{π σ}}$

d

$\sqrt{\frac{mg}{2 π σ}}$

answer is D.

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Detailed Solution

Maximum stress is developed in the topmost section.

$∴ (\frac{π}{4} d^{2}) σ = mg \Rightarrow d = \sqrt{\frac{4 mg}{π σ}}$

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Maximum tensile stress that a material can withstand is σ. A rod of mass m having uniform cross sectional area, made of the above mentioned material is freely suspended from one end. Then find its minimum diameter.