A bomb of mass $9\, kg$ explodes into two pieces of masses $3\, kg$ and $6\, kg$. The velocity of mass $3\, kg$ is $16\, m/s$. The $KE$ of mass $6\, kg$ is ............ $\mathrm{J}$
$96$
$384$
$192$
$768$
$A$ block of mass $m$ starts from rest and slides down $a$ frictionless semi-circular track from $a$ height $h$ as shown. When it reaches the lowest point of the track, it collides with a stationary piece of putty also having mass $m$. If the block and the putty stick together and continue to slide, the maximum height that the block-putty system could reach is:
A mass $M$ moving with a certain speed $V$ collides elastically with another stationary mass $m$. After the collision, the masses $M$ and $m$ move with speeds $V^{\prime}$ and $v$, respectively. All motion is in one dimension. Then,
Write the equation of total mechanical energy of a body having mass $m$ and stationary at height $H$.
Write the law of conservation of total linear momentum for the system of particle.
Given in Figures are examples of some potential energy functions in one dimension. The total energy of the particle is indicated by a cross on the ordinate axis. In each case, specify the regions, if any, in which the particle cannot be found for the given energy. Also, indicate the minimum total energy the particle must have in each case. Think of simple physical contexts for which these potential energy shapes are relevant.