A smooth sphere $A$ of mass $m$ collides elastically with an identical sphere $B$ at rest. The velocity of $A$ before collision is $8\ m/s$ in a direction making $60^o$ with the line of centres at the time of impact.

$(i)$ The sphere $A$ comes to rest after collision.

$(ii)$ The sphere $B$ will move with a speed of $8\ m/s$ after collision.

$(iii)$ The directions of motion $A$ and $B$ after collision are at right angles.

$(iv)$ The speed of $B$ after collision is $4\ m/s$ . The correct option is 

$A$ ball is of mass $m$, strikes a smooth ground at angle $\alpha$ as shown in figure and is deflected at angle $\beta$. The coefficient of restitution will be

A particle of mass $1\, kg$ moving with velocity $1\, m/s$, collides elastically with another particle of mass $m$. In the collision particle of mass $1\, kg$ loses $\frac{3}{4}$of its $K.E.$ The value of $m$ is :

$A$ ball strikes a smooth horizontal ground at an angle of $45^o$ with the vertical. What cannot be the possible angle of its velocity with the vertical after the collision ................. $^o$ (Assume $e \leq 1$ ).

In the figure shown, a small ball hits obliquely a smooth and horizontal surface with speed $u$ whose $x$ and $y$ components are indicated. If the coefficient of restitution is $\frac{1}{2}$, then its $x$ and $y$ components $v_x$ and $v_y$ just after collision are respectively

$A$ flexible chain of length $2m$ and mass $1kg$ initially held in vertical position such that its lower end just touches a horizontal surface, is released from rest at time $t = 0$. Assuming that any part of chain which strikes the plane immediately comes to rest and that the portion of chain lying on horizontal surface does not from any heap, the height of its centre of mass above surface at any instant $t = 1/\sqrt 5$ befor it completely comes to rest) is ................ $\mathrm{m}$