Three identical balls are connected by light inextensible strings with each other as shown and placed over a smooth horizontal table. Length of each string is $l$ .
At moment $t = 0$ , ball B is imparted a velocity $v_{0}$ perpendicular to the string and then the system is left on its own. The speed of A at the instant just before it collides with C is

Question

Three identical balls are connected by light inextensible strings with each other as shown and placed over a smooth horizontal table. Length of each string is

l

.
At moment

t = 0

, ball B is imparted a velocity

v_{0}

perpendicular to the string and then the system is left on its own. The speed of A at the instant just before it collides with C is

Aicharya · Accepted Answer

Using conservation of linear momentum along the initial direction of motion of $B$ we get,

$m v_{0} = 3 m v$

$v = \frac{v_{0}}{3}$

The total kinetic energy of the system will remain the same

$\frac{1}{2} m v_{0}^{2} = \frac{1}{2} m v^{2} + 2 [\frac{1}{2} m (v^{2} + v_{1}^{2})]$

where $v_{1}$ is the component of velocity of $A$ and $C$ perpendicular to the initial direction of motion of $B$

$v_{0}^{2} = {(\frac{v_{0}}{3})}^{2} + 2 {(\frac{v_{0}}{3})}^{2} + 2 v_{1}^{2}$

$v_{1}^{2} = \frac{v_{0}^{2}}{3}$

Velocity of $A = \sqrt{v^{2} + v_{1}^{2}} = \frac{2}{3} v_{0}$

Three identical balls are connected by light inextensible strings with each other as shown and placed over a…

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