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Mass M is uniformly distributed over a circular arc of radius R. Then

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Net Gravitational field intensity at ‘O’ in X direction is zero, when $α = β$ .

Net gravitational field intensity at ‘O’ in Y direction is zero if $α = β$

If $α = β = \frac{π}{2},$ then at ‘O’ $I_{x} = 0$ and $I_{y} = \frac{2 G λ}{R}$

If $α = β = π,$ then at ‘O’ $I_{x} = I_{y} = 0$

answer is A.

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Detailed Solution

$E_{y} = \frac{G λ}{R} [\sin α + \sin β]; E_{x} = \frac{G λ}{R} [\cos α - \cos β]$

$(a) If α = β \Rightarrow E_{x} = 0$

$(b) If α = β \Rightarrow E_{y} = \frac{2 G λ}{R} \sin α \neq 0$

$(c) If α = β = \frac{π}{2} \Rightarrow E_{x} = 0 & E_{y} = \frac{2 G λ}{R}$

$(d) If α = β = π \Rightarrow E_{x} = 0 & E_{y} = 0$

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