Q.

A thin wire of length L and mass M  is bent to form a semicircle. What is the gravitational field at the centre.

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a

πGM/L2  among the line joining the ends

b

πGM/L2 perpendicular to the above line.

c

 2πGM/L2 along the line joining the ends.

d

2πGM/L2 perpendicular to the above line.

answer is D.

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Detailed Solution

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Question Image 

Enet=0π/22dEcosα

dEsinα  will be cancelled due to symmetry.
E=2Gmπ00π/2cosαdα(Lπ)2       dm=Mπdα   
   R=Lπ
=2πΓΜL2 (along  G to live joining the ends)

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