The law of conservation of linear momentum is derived by using which of Newton's laws?

$A$ person of mass $M=90 \ kg$ standing on a smooth horizontal plane of ice throws a body of mass $m=10 \ kg$ horizontally on the same surface. If the distance between the person and the body after $10 \ s$ is $10 \ m$,then the kinetic energy $(KE)$ of the person (in $J$) is: (in $J$)

$A$ bomb of mass $12 \ kg$ initially at rest explodes into two fragments with a mass ratio of $1:3$. The kinetic energy of the smaller fragment is $216 \ J$. What is the momentum of the larger (heavier) fragment in $kg \cdot m/s$?

$A$ bomb at rest explodes into $3$ parts of the same mass. The momentum of two parts is $-3 p \hat{i}$ and $2 p \hat{j}$ respectively. The magnitude of the momentum of the third part is

$A$ man of mass $m_1$ is standing on a platform of mass $m_2$ kept on a smooth horizontal surface. If the man starts moving on the platform with a velocity $v$ relative to the platform,then the recoil velocity of the platform is:

$A$ stationary particle breaks into two parts of masses $m_A$ and $m_B$ which move with velocities $v_A$ and $v_B$ respectively. The ratio of their kinetic energies $(K_B : K_A)$ is