Question

The bob $A$ of a pendulum of mass $m$ released from horizontal to the vertical hits another bob $B$ of the same mass at rest on a table as shown in figure. If the length of the pendulum is $1m$, what is the speed with which bob $B$ starts moving. (Neglect the size of the bobs and assume the collision to be elastic) (Take $g=10m{s}^{-2})$.

• A. $4.47m{s}^{-1}$
• B. $5.47m{s}^{-1}$
• C. $6.47m{s}^{-1}$
• D. $3.47m{s}^{-1}$

Answer 1

The correct option is A $4.47m{s}^{-1}$

As the collision is elastic and two balls have the same mass, therefore ball $A$ transfers its entire momentum to the ball $B$ and ball $A$ does not rise at all. After a collision, ball $A$ comes to rest and ball $B$ moves with speed of ball $A$.
$\therefore$ The speed with which bob $B$ starts moving is
$v=\sqrt{2gh}$

$=\sqrt{2\times 10m{s}^{-2}\times 1m}=\sqrt{20}m{s}^{-1}$

$=4.47m{s}^{-1}$