$A$ body of mass $4 \,kg$ is moving with momentum of $8 \,kg \,m/s$. $A$ force of $0.2 \,N$ acts on it in the direction of motion of the body for $10 \,s$. The increase in kinetic energy in joules is

$A$ body $A$ moving with momentum $P$ collides one-dimensionally with another stationary body $B$ of same mass. During impact,$A$ gives impulse $J$ to $B$. Then which of the following is/are correct?
$(a)$ The total momentum of $A$ and $B$ is $P$ before and after impact and $(P-J)$ during the impact.
$(b)$ During the impact,$B$ gives impulse of magnitude $J$ to $A$.
$(c)$ The coefficient of restitution is $\left[\frac{2 J}{P}-1\right]$.
$(d)$ The coefficient of restitution is $\left[\frac{2 J}{P}+1\right]$.

$A$ particle of mass $m$ moving eastward with a speed $v$ collides with another particle of same mass moving northward with same speed $v$. The two particles coalesce after collision. The new particle of mass $2m$ will move in north-east direction with a speed (in $m/s$) of:

An object of mass $M$ is at rest on a smooth horizontal surface. Objects of different masses collide head-on elastically with the object of mass $M$. All colliding objects have the same fixed kinetic energy $E$,and in each case,mass $M$ is initially at rest. The kinetic energy transferred to the stationary mass $M$ depends on the linear momentum $P$ of the incoming colliding mass. How does the energy transferred to $M$ vary with the linear momentum $P$?

$A$ wedge of mass $M = 4m$ lies on a frictionless plane. $A$ particle of mass $m$ approaches the wedge with speed $v$. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by

Three blocks $A, B$ and $C$ are lying on a smooth horizontal surface,as shown in the figure. $A$ and $B$ have equal masses $m$,while $C$ has mass $M$. Block $A$ is given an initial speed $v$ towards $B$,due to which it collides with $B$ perfectly inelastically. The combined mass then collides with $C$,also perfectly inelastically. If $5/6^{th}$ of the initial kinetic energy is lost in the whole process,what is the value of $M/m$?