IIT JEE , AIEEE Forum - Physics , Mechanics

ayushmundhra

A particle moves along a closed trajectory in a central field of force where the

particle's potential energy U=kr²kis a positive const. r is the radius of the particle frm the centre of the force field.Find the mass of the particle if its minimum distance is r₁and its velocity at the farthest point is v_2.

Ans. 2k (r₁/ v₂)²

I want the working wid proper explanation...

karthik2007

It is quite simple.

Now let us choose the farthest point as the zero of potential energy.

Also, here velocity is v₂.
So net energy here is 1/2mv₂² + 0 (PE is zero as we have chosen this to be reference point).

Consider the point at a distance r₁.

Net energy here is Kr₁² (Its not given that the particle moves here, so kinetic energy is zero)

As there is no external force, use conservation of energy

Kr₁² = 1/2mv₂²

Which gives m = 2k(r₁/v₂)².

karthik2007

I hope everything is clear

frenied

i have a little doubt......-dU/dr is supposed to give force which as appears is not zero....so how have u assumed that the force is zero??

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