The bob $A$ of a pendulum 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 $1\,m$, calculate
$(a)$ the height to which bob $A$ will rise after collision.
$(b)$ the speed with which bob $B$ starts moving.
Neglect the size of the bobs and assume the collision to be elastic.
The bob $A$ of a pendulum 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 $1\,m$, calculate
$(a)$ the height to which bob $A$ will rise after collision.
$(b)$ the speed with which bob $B$ starts moving.
Neglect the size of the bobs and assume the collision to be elastic.
When ball $A$ reaches bottom point its velocity is horizontal, hence, we can use law of conservation of linear momentum in the horizontal direction.
$(a)$ Two balls have same mass and the collision between them is elastic, therefore, ball $A$ transfers its entire linear momentum to ball $B$. Hence, ball $A$ will come to at rest after collision.
$(b)$ Speed with which boLL $B$ starts moving
$=\text { Speed with which bob A hits boll B }$
$=\sqrt{2 g h}$
$=\sqrt{2 \times 9.8 \times 1}$
$=\sqrt{19.6}$
$=4.42 \mathrm{~m} / \mathrm{s}$
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