Gravitation Question 341

Question: Gravitational field at the centre of a semicircle formed by a thin wire AB of mass m and length [] is

Options:

A) [Gm2along+xaxis]

B) [Gmπ2along+yaxis]

C) [2πGm2along+xaxis]

D) [2πGm2along+yaxis]

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Answer:

Correct Answer: D

Solution:

  • Let mass per unit light of wire, [λ=M]

    and [πr=,r=π] .

    mass of element,

    [dm=λrdθ then dE=Gdmr2]

    [0πdE0πGλrdθr2(i^cosθ+j^sinθ)]

    [E=Gλr[0πi^cosθ+0πj^sinθ]]

    [=2Gλrj^=2GMrj^=2Gmπ2j^] (along y-axis



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