33Its is obvious 4 electrostatic force but 4 gravitational force.....
let me see....
a body whose dimensions may be neglected is placed inside a thin homogenious sphere.prove that the force of attraction acting from the sphere on the body is zeroirrespesctive of its position inside the sphere!
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10 Answers
3333A similar theory for gravitational flux.....
will prove that.
total flux crossing an enclosed surface is 4piGm
m is mass enclosed here it is zero so flux is zero so ∫E.dS=0
here E=0.....
Ne one has some other method...........
39but i have the same method with a totalyyyyyyyyyyyyyyyyyyyyyyyyyyy different approach
39[the sought force of attraction is the geometrical sum of the forces created by the separate elements of the sphere.the small elements σ1 and σ2 are cut out of the sphere as cones with vertices at point A obtained when the generatrix BC revolves around the axis S1S2. The areas of the elements are (AS1).(AS1)ω/COSα1 and (AS2)(AS2)ω/COSα2 RESPECTIVELY and their masses are (AS1)(AS1)ωÏ/COSα1 AND (AS2)(AS2)ωÏ/COSα2 ;where ω is the solid angles at which both the elements can be seen from the point A;Ï IS THE MASS PER UNIT OF SURFACE THE SPHERE.
now, α1=α2 since S1OS2 is an isosceles triangle.the forces of attraction created by the sphere are equal,respectively to
γmÏω/cosα1 and
γmÏω/cosα2 where `m` is the mass of the body.these forces act in opposite direction and their resultant is zero.
reasoning in the same way for all the other corresponding elements of the of the sphere,we can say that all of them compensate one another in pairs.
therefore the force of attraction acting from the sphere on the body is zero.
62This is an elegant proof of this problem.. i wud surely have not been able to think of this one myself..
well done buddy :)