Which of the following graphs represents the graphical relation between momentum $(p)$ and kinetic energy $(K)$ for a body in motion?

Two particles of the same mass are moving in circular orbits because of force, given by $F(r) = \frac{{ – 16}}{r}\, – \,{r^3}$ The first particle is at a distance $r = 1,$  and the second, at $r = 4.$  The best estimate for the ratio of kinetic energies of the first and the second particle is closest to

Four particles $A, B, C, D$ of mass $\frac{\mathrm{m}}{2}, \mathrm{~m}, 2 \mathrm{~m}, 4 \mathrm{~m}$, have same momentum, respectively. The particle with maximum kinetic energy is:

A point particle of mass $0.5 \,kg$ is moving along the $X$-axis under a force described by the potential energy $V$ shown below. It is projected towards the right from the origin with a speed $v$. What is the minimum value of $v$ for which the particle will escape infinitely far away from the origin?

An electron and a proton are detected in a cosmic ray experiment, the first with kinetic energy $10\; keV$, and the second with $100\; keV$. Which is faster, the electron or the proton? Obtain the ratio of their speeds. (electron mass $=9.11 \times 10^{31}\; kg$. proton mass $=1.67 \times 10^{-27}\;$$ kg , 1 \;eV =1.60 \times 10^{-19} \;J )$