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Two identical ball bearings in contact with each other and resting on a frictionless table is hit head-on by another ball bearing of the same mass moving initially with a speed $V$. If the collision is elastic, which of the following figure is a possible result after collision?
Two identical ball bearings in contact with each other and resting on a frictionless table is hit head-on by another ball bearing of the same mass moving initially with a speed $V$. If the collision is elastic, which of the following figure is a possible result after collision?
CBSE | Class 11 | NCERT | Physics | Work, Energy, and Power
Two identical ball bearings in contact with each other and resting on a frictionless table is hit head-on by another ball bearing of the same mass moving initially with a speed $V$. If the collision is elastic, which of the following figure is a possible result after collision?

Solution:

The mass of the ball bearing is given as $\mathrm{m}$

Before the collision, Total Kinetic Energy of the system will be

$=1 / 2 m v^{2}+0=1 / 2 m v^{2}$

After the collision, Total Kinetic Energy of the system is

Case I, $E_{1}=(1 / 2)(2 m)(v / 2)^{2}=1 / 4 \mathrm{mv}^{2}$

Case II, $E_{2}=(1 / 2) \mathrm{mv}^{2}$

Case III, $\mathrm{E}_{3}=(1 / 2)(3 \mathrm{~m})(\mathrm{v} / 3)^{2}=3 \mathrm{mv}^{2} / 18=1 / 6 \mathrm{mv}^{2}$

Thus, case II is the only possibility since K.E. is conserved in this case.

Thus,

is only possible since KE of the system is conserved

i

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