Question

The ratio momentum and kinetic energy of a particle is inversely proportional to the time. This is the case of a

• A. uniformly acceleration motion
• B. uniform motion
• C. uniformly retarded motion
• D. simple harmonic motion

Answer 1

The correct option is A uniformly acceleration motion

The ratio of momentum $(=mv)$ and kinetic energy $(=\frac{1}{2}m{v}^2)$

in inversely proportional to time ie:-

$\frac{mv}{\frac{1}{2}m{v}^2}\alpha \frac{1}{t}\Rightarrow v=\frac{t}{2k}$ [k = constant of proportionality]

differentiate both sides wrt to time,

$a=\frac{dv}{dt}=\frac{1}{2k},$ as a = constant $\Rightarrow$ uniformly acclted. motion.