Choose the correct statement(s)

Options

A. (a) Force acting on a particle for equal time intervals can produce the same change in momentum but different change in kinetic energy.
B. (b) Force acting on a particle for equal displacemenets can produce same change in kinetic energy but different change in momentum.
C. (c) Force acting on a particle for equal time intervals can produce different change in momentum but same change in kinetic energy.
D. (d) Force acting on a particle for equal displacements can produce different change in kinetic energy but same change in momentum.

Answer

A, B

Explanation

The change in momentum for each time interval `t_0` is
`Deltap=Ft_0` which is constant.
But the change in kinetic energy in each time interval `t_0` is different.
First `t_0` interval: `DeltaK_1=(Deltap^2)/(2m)=(F^2t_0^2)/(2m)`
Secon `t_0` interval: `DeltaK_2=((2Deltap)^2-(Deltap)^2)/(2m)=(3F^2t_0^2)/(2m)`
The change in kinetic energy is `DeltaK=Fx_0=const ant`.
First `x_0` displacement: `Deltap_1=sqrt(2mDeltaK_1)=sqrt(2m(Fx_0))`
Second `x_0` displacement:
`Deltap_2=sqrt(2m(2Fx_0))-sqrt(2m(Fx_0))=0.414sqrt(2m(Fx_0))`