Grade 11Mechanics
What is the Gravitational field at the centre of a semicircle formed by a thin wire AB of mass m and length L ?
What is the Gravitational field at the centre of a semicircle formed by a thin wire AB of mass m and length L ?
1 Answer
Vikas TU
Let at dθ angle dm mass element cut thorugh and then integerate it for semicircle.
Then dm mass would be:
dm = (m/π)*dθ
Gravitaonal foeld for this small element would be:
dg = Gmdθ/(πR^2)
Horizontal componet would be
dgcosthetha
and verical component would be
dgsinthetha
so therefore, vertical components would get added and horizontal ones would cancel out.
gnet = integeration(dgsin(thetha))
putting the value and ineterating we get,
gnet = (G*m*sinθ*dθ)/(πR^2)
=> 2*pi*G*m/l^2 (take limits from pi to 0.)
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