A bomb of mass $12\,\,kg$  at rest explodes into two fragments of masses in the ratio $1 : 3.$  The $K.E.$  of the smaller fragment is $216\,\,J.$  The momentulm of heavier fragment is (in $kg-m/sec$ )

Write the equation of total mechanical energy of a body having mass $m$ and stationary at height $H$.

A particle of mass $m$ moving horizontally with $v_0$ strikes $a$ smooth wedge of mass $M$, as shown in figure. After collision, the ball starts moving up the inclined face of the wedge and rises to $a$ height $h$. When the particle has risen to $a$ height $h$ on the wedge, then choose the correct alternative $(s)$

In the figure shown, a particle is released from the position $A$ on a smooth track. When the particle reaches at $B$, then normal reaction on it by the track is .........

In a system of particles, internal forces can change (for the system)

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