In case of a perfectly elastic collision,

$A$ ball of mass $m$ moving with speed $u$ collides with a smooth horizontal surface at an angle $\theta$ with it as shown in the figure. The magnitude of the impulse imparted to the surface by the ball is [Coefficient of restitution of collision is $e$].

$A$ 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 $cm$)

$A$ ball of mass $1 \ kg$ moving along the $X$-direction collides elastically with a stationary ball of mass $m$. The first ball (mass $= 1 \ kg$) recoils at a right angle to its original direction of motion. If the second ball starts moving at an angle $30^{\circ}$ with the $X$-axis,the value of $m$ must be (in $kg$)

$A$ body $A$ of mass $m=0.1 \; kg$ has an initial velocity of $3 \hat{i} \; ms^{-1}$. It collides elastically with another body $B$ of the same mass which has an initial velocity of $5 \hat{j} \; ms^{-1}$. After the collision,$A$ moves with a velocity $\vec{v}_A = 4(\hat{i} + \hat{j}) \; ms^{-1}$. The energy of $B$ after the collision is written as $\frac{x}{10} \; J$. The value of $x$ is:

Particle $A$ makes a perfectly elastic collision with another particle $B$ at rest. They fly apart in opposite directions with equal speeds. If their masses are $m_A$ and $m_B$ respectively,then: