State and establish principle of conservation of mechanical energy.

$Assertion$ : A helicopter must necessarily have two propellers.
$Reason$ : Two propellers are provided in helicopter in order to conserve linear momentum

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 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 spaceship of speed $v_0$ travelling along $+ y$ axis suddenly shots out one fourth of its part with speed $2v_0$ along $+ x$ -axis. $xy$ axes are fixed with respect to ground. The velocity of the remaining part is

A light spring of length $20\, cm$ and force constant $2\, kg/cm$ is placed vertically on a table. A small block of mass $1\, kg$. falls on it. The length $h$ from the surface of the table at which the ball will have the maximum velocity is ............... $\mathrm{cm}$