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Question

Gravitational field at the centre of semicircle formed by a thin wire AB of mass m and length l is


A

GMl2 along x - axis

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B

GMπl2 along y - axis

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C

2πGMl2

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D

2πGMl2

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Solution

The correct option is D

2πGMl2


F = dF cosθ = GMDMr2 cos θ

= GMr2 π2π2 mπr . r d θ . cos θ d θ

= GMπr2 π2π2 cos θ d θ

= 2GMmπr2

= 2gMmπ(lπr)2 = 2πGMml2

Gravitational Field = Fm


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