A particle of mass M moves along a straight line with initial speed vi. A force of magnitude F pushes the particle a distance D along the direction of its motion. Required:
By what multiplicative factor RK does the initial kinetic energy increase, and by what multiplicative factor RWdoes the work done by the force increase (with respect to the case when the particle had a mass M)?

Solution :

From the Newton's second law of motion :

F = ma

Integrating above the expression by applying the limits :

Here the diameter is s= D

The final speed of the particle after travelling distance D is

The kinetic energy of the particle of mass M is :

For M = 3M

Thus the kinetic energy increases by a factor of 3.

The work done depends on the factor and the displacement of the body. Thus, the work done remains same even though the mass increases. Hence the work down increases by factor 1.