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?

Asked by Pragya Singh | 1 year ago | 59

The mass of the ball bearing is m

Before the collision, Total K.E. of the system

=\( \dfrac{1}{2}\)mv^{2} + 0 =\( \dfrac{1}{2}\) mv^{2}

After the collision, Total K.E. of the system is

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

Case II, E_{2} =( \( \dfrac{1}{2}\)) mv^{2}

Case III, E_{3} = (\( \dfrac{1}{2}\)) (3m) \(( \dfrac{v}{3})^2\)

=\( \dfrac{3mv^2}{18}=\dfrac{1}{6}mv^2\)

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

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