When does the maximum energy transfer occur during an elastic collision?

$A$ body $A$ of mass $4m$ moving with speed $u$ collides with another body $B$ of mass $2m$,which is at rest. The collision is head-on and elastic in nature. After the collision,the fraction of energy lost by the colliding body $A$ is

$A$ smooth sphere $A$ is moving on a frictionless horizontal plane with an angular velocity $\omega$ and its center of mass is moving with a linear velocity $v$. It undergoes an elastic collision with a stationary sphere $B$. (Ignore friction everywhere). If the angular speeds after the collision are $\omega_A$ and $\omega_B$ respectively,then:

Two identical spheres move in opposite directions with speeds $v_1$ and $v_2$ and pass behind an opaque screen,where they may either cross without touching (Event $1$) or make an elastic head-on collision (Event $2$).

$A$ body of mass $M$ moving at speed $V_{0}$ collides elastically with a mass $m$ at rest. After the collision,the two masses move at angles $\theta_{1}$ and $\theta_{2}$ with respect to the initial direction of motion of the body of mass $M$. The largest possible value of the ratio $M/m$,for which the angles $\theta_{1}$ and $\theta_{2}$ will be equal,is:

$A$ particle of mass $m$ moving with a speed $v$ hits elastically another stationary particle of mass $2m$ in a fixed smooth horizontal circular tube of radius $R$. Find the time when the next collision will take place?