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 lift of mass $M =500\,kg$ is descending with speed of $2\,ms ^{-1}$. Its supporting cable begins to slip thus allowing it to fall with a constant acceleration of $2\,ms ^{-2}$. The kinetic energy of the lift at the end of fall through to a distance of $6 m$ will be $………..kJ.$

A block moving horizontally on a smooth surface with a speed of $40\, {m} / {s}$ splits into two parts with masses in the ratio of $1: 2$. If the smaller part moves at $60\, {m} / {s}$ in the same direction, then the fractional change in kinetic energy is :-

A particle of mass $'m'$ and charge $'q'$ is accelerated through a potential difference of $'V'$ volt. Its energy is

A bomb of mass $16\ kg$ at rest explodes into two pieces of masses $4\ kg$ and $12\ kg.$ The velolcity of the $12\ kg$ mass is $4$ $ms^{-1}$. The kinetic energy of the other mass is ………….. $\mathrm{J}$