Two identical ball bearings in contact with ...

Work, Power and Energy

Question : 16 of 30

Marks: +1, -0

Two identical ball bearings in contact with each other and resting on a frictionless table are 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 possibleresult after collision?

Solution:

m is the mass of each ball bearing.

Total kinetic energy of the system before collisions

E= \frac{1}{2} m v^{2}+0= \frac{1}{2} m v^{2}

Kinetic energy of the system after collision

Case I :

E= \frac{1}{2}(2 m) \times \left( \frac{v}{2} \right)^{2}= \frac{1}{4} m v^{2}

Case II :

E_{2}= \frac{1}{2} m v^{2}

Case III :

E_{3}= \frac{1}{2}(3 m) \left( \frac{v}{3} \right)^{2}= \frac{1}{6} m v^{2}

We observe that kinetic energy is conserved before collision as well as after collision only in Case II. Therefore Case II is the only possibility.

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