Two particles of masses $m_1, m_2$ move with initial velocities $u_1$and $u_2$ On collision, one of the particles get excited to higher level, after absorbing energy $\varepsilon $. If final velocities of particles be $v_1$ and $v_2$ then we must have
$\frac{1}{2}{m_1}{u_1}^2 + \frac{1}{2}{m_2}{u_2}^2 = \frac{1}{2}{m_1}{v_1}^2 + \frac{1}{2}{m_2}{v_2}^2 - \varepsilon $
$\;\frac{1}{2}{m_1}{u_1}^2 + \frac{1}{2}{m_2}{u_2}^2 - \varepsilon = \frac{1}{2}{m_1}{v_1}^2 + \frac{1}{2}{m_2}{v_2}^2$
$\;\frac{1}{2}{m_1}{u_1}^2 + \frac{1}{2}{m_2}{u_2}^2 + \varepsilon = \frac{1}{2}{m_1}{v_1}^2 + \frac{1}{2}{m_2}{v_2}^2$
$m_1^2u_1+m_2^2u_2 - \varepsilon = m_1^2v_1+m_2^2v_2$
A ball is allowed to fall from a height of $10 \,m$. If there is $40 \%$ loss of energy due to impact, then after one impact ball will go up by ........ $m$
A ball is thrown from $10\,m$ height at speed $v_0$ vertically downward. In colliding surface of earth it looses $50\%$ of its energy and again reach upto same height. Value of $v_0$ is :- .................$\mathrm{m}/ \mathrm{s}$
An object flying in alr with velocity $(20 \hat{\mathrm{i}}+25 \hat{\mathrm{j}}-12 \hat{\mathrm{k}})$ suddenly breaks in two pleces whose masses are in the ratio $1: 5 .$ The smaller mass flies off with a velocity $(100 \hat{\mathrm{i}}+35 \hat{\mathrm{j}}+8 \hat{\mathrm{k}}) .$ The velocity of larger piece will be
A small ball falling vertically downward with constant velocity $4m/s$ strikes elastically $a$ massive inclined cart moving with velocity $4m/s$ horizontally as shown. The velocity of the rebound of the ball is
$A$ projectile of mass $"m"$ is projected from ground with a speed of $50 \,m/s$ at an angle of $53^o$ with the horizontal. It breaks up into two equal parts at the highest point of the trajectory. One particle coming to rest immediately after the explosion. The distance between the pieces of the projectile when they reach the ground are: