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A chain of mass per unit length $λ$ and length 1.5m rests on a fixed smooth sphere of radius $R = \frac{2}{π}$ m such that end A of chain is at the top of sphere while the other end is hanging freely. Chain is held stationary by a horizontal thread PA. The tension in the thread (in SI units) is

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$λ g (\frac{π}{2})$

$λ g (\frac{π}{2} + \frac{2}{π})$

$λ g (\frac{1}{2} + \frac{2}{π})$

$λ g (\frac{2}{π})$

answer is A.

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Detailed Solution

$d T = (d m) g \sin θ$

$d t = λ R g \sin θ d θ$

$\int_{T_{1}}^{T_{2}} d T = λ R g \int_{0}^{π / 2} \sin θ d θ$

$T_{2} - T_{1} = λ R g$

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