Question

If the ratio of momentum and kinetic energy of a particle is inversely proportional to the square of the time, then it is the case of

• A. constant force
• B. force decreasing with time
• C. force increasing with time
• D. simple harmonic motion

Answer 1

The correct option is C force increasing with time

Force = rate of change of momentum
Given,
$\frac{p}{K}=\frac{1}{c{t}^2}$

$K=pc{t}^2$

$\frac{p^2}{2m}=pc{t}^2$

$p=2mc{t}^2$

$F=\frac{dp}{dt}=4mct$

$Force\propto time$