A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows that

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 )$

A bomb is kept stationary at a point. It suddenly explodes into two fragments of masses $1\, g$ and $3\;g$. The total K.E. of the fragments is $6.4 \times {10^4}J$. What is the K.E. of the smaller fragment

A particle of mass $m$ is initially at rest at the origin. It is subjected to a force and starts moving along the $x$-axis. Its kinetic energy $K$ changes with time as $dK / dt =\gamma$ t, where $\gamma$ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

$(A)$ The force applied on the particle is constant

$(B)$ The speed of the particle is proportional to time

$(C)$ The distance of the particle from the origin increases linearly with time

$(D)$ The force is conservative

Two bodies of masses ${m_1}$ and ${m_2}$ have equal kinetic energies. If ${p_1}$ and ${p_2}$ are their respective momentum, then ratio ${p_1}:{p_2}$ is equal to

The kinetic energy $k$ of a particle moving along a circle of radius $R$ depends on the distance covered $s$ as $k = a{s^2}$ where $a$ is a constant. The force acting on the particle is