A body initially at rest, breaks up into two pieces of masses $2 M$ and $3 M$ respectively, together having a total kinetic energy $E$. The piece of mass $2 M$, after breaking up, has a kinetic energy

An object of mass ' $m$ ' initially at rest on a smooth horizontal plane starts moving under the action of force $F=2 N$. In the process of its linear motion, the angle $\theta$ (as shown in figure) between the direction of force and horizontal varies as $\theta= kx$, where $k$ is a constant and $x$ is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be $E =\frac{ n }{ k } \sin \theta$. The value of $n$ is $.....$

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 )$

Consider the following two statements
$1.$ Linear momentum of a system of particles is zero
$2.$ Kinetic energy of a system of particles is zeroThen

A bomb of mass $30\,kg$at rest explodes into two pieces of masses $18\,kg$ and $12\,kg$. The velocity of $18\,kg$ mass is $6\,m{s^{ - 1}}$. The kinetic energy of the other mass is ....... $J$

A ball is thrown up with a certain velocity at an angle $\theta$ to the horizontal. The kinetic energy $KE$ of the ball varies with horizontal displacement $x$ as