When a ball is freely fallen from a given height,it bounces to $80\%$ of its original height. What fraction of its mechanical energy is lost in each bounce?

Five masses,each of $2 \, kg$,are placed on a horizontal circular disc that can rotate about a vertical axis passing through its centre. All the masses are equidistant from the axis at a distance of $10 \, cm$. The moment of inertia of the whole system (in $g \cdot cm^2$) is (Assume the disc has negligible mass).

Two particles of masses $m_1$ and $m_2$ are separated by a distance $d$. The shift in the centre of mass when the two particles are interchanged is:

Which of the following is the most important cause for the extinction of animals and plants?

If $3$ is a root of $x^2+kx-24=0$,then it is also a root of which of the following equations?

$A$ cannon shell fired breaks into two equal parts at its highest point. One part retraces its path to the cannon with kinetic energy $E_1$,and the kinetic energy of the second part is $E_2$. The relation between $E_1$ and $E_2$ is: