When a particle of mass m is at (x,0), it is attracted toward the origin with a force whose magnitude is k/x^2 where k is some constant. if a particle starts from rest at x = b and no other forces act on it, calculate the work done on it by the time it reaches x = a, 0 < a < b.

Explanation:

Given:

Force,

Now we know,

work done, W = Force × Displacement

Now for the small displacement, dx the work done will be

W=F.dx

Now for the work done from 'a' to 'b' will be

or

now for the given condition 0<a<b , and the particle is moving from point b to the point 'a'

thus, the work done will be negative

therefore,

or

or

or

or

or

 (Answer)

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