In the elastic collision of objects,

$A$ body of mass $8 \ kg$ moving with a certain velocity collides elastically with another body of mass $2 \ kg$ at rest. If $E$ is the initial kinetic energy of the moving mass,what will be the remaining kinetic energy of the moving mass after the collision (in $E$)?

$A$ body of mass $5 \ kg$ makes an elastic collision with another body at rest and continues to move in the original direction after collision with a velocity equal to $\frac{1}{10}$ th of its original velocity. Then the mass of the second body is (in $kg$)

$A$ steel sphere of radius $1.2 \ cm$ collides with a second steel sphere at rest. If the collision is elastic and after the collision the first sphere continues to move in its initial direction with a velocity of $\frac{7}{9}$ times its initial velocity,then the radius of the second sphere is (in $cm$)

$A$ particle of mass $m$ moving with a velocity $u$ makes an elastic one-dimensional collision with a stationary particle of mass $m$. They are in contact for a total time $T$. The contact force increases linearly from $0$ to $F_0$ in time $\frac{T}{4}$, remains constant for a further time $\frac{T}{2}$, and decreases linearly from $F_0$ to $0$ in the final time $\frac{T}{4}$, as shown in the graph. The magnitude of $F_0$ is:

$A$ ball of $0.4 \, kg$ mass and a speed of $3 \, m/s$ has a head-on,completely elastic collision with a $0.6 \, kg$ mass initially at rest. Find the speeds of both balls after the collision: