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)

the second one and the forth one are in the purple because they are opinions and the rest are in the yellow

explanation:

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.