As per the given figure, two blocks each of mass $250\,g$ are connected to a spring of spring constant $2\,Nm ^{-1}$. If both are given velocity $V$ in opposite directions, then maximum elongation of the spring is:

A particle of mass $m$ travelling along $x-$ axis with speed $v_0$ shoots out $1/3^{rd}$ of its mass with a speed $2v_0$ along $y-$ axis. The velocity of remaining piece is

A body of mass $50\, kg$ is projected vertically upwards with velocity of $100 \,m/sec$. $5 \,seconds$ after this body breaks into $20\, kg$ and $30 \,kg$. If $20\, kg $ piece travels upwards with $150 \,m/sec$, then the velocity of other block will be

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 $kg-m/sec$ )

A person trying to lose weight (dieter) lifts a $10\; kg$ mass, one thousand times, to a hetght of $0.5\; m$ each time. Assume that the potential energy lost each time she lowers the mass is dissipated.

$(a)$ How much work does she do against the gravitational force?

$(b)$ Fat supplies $3.8 \times 10^{7} \;J$ of energy per kilogram which is converted to mechanical energy with a $20 \%$ efficiency rate. How much fat will the dieter use up?

Write the principle of conservation of mechanical energy for non-conservative force.