Question

# Gravitational field at the center of the semicircle formed by thin wire AB of mass m and length l as shown in the figure is:- A
Gml2along+xaxis
B
Gmπl2along+yaxis
C
2πGml2along+xaxis
D
2πGml2along+yaxis
Solution
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#### The correct option is D2πGml2along+yaxisMass of element dm=m1xdθGravitational field due to element dg=GdmR2=GmdθπR2dgcosθ of each element will be cancelled out δ=∫dgsinθ =∫π0(sinθπR2)sinθ =GmπR2∫π0sinθdθ =2GmπR2 =2πGml2 along+yaxis 2
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