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  • 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 as shown in Figure.

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 as shown in Figure.

If the collision is elastic, which of the following (Figure) is a possible result after collision?

 

Answers (1)

The answer is the option (b)

In an elastic collision, the velocities of particles are interchanged while the kinetic energy and total linear momentum are conserved.

Kinetic energy before collision:

\frac{1}{2} mv^{2} + 0 = \frac{1}{2} mv^{2}

Option a) Kinetic energy after the collision:

Ka = \frac{1}{2} (2m) \left ( \frac{v}{2} \right )^{2} = \frac{1}{4} mv^{2}

Option b) Kinetic energy after the collision:

  Ka = \frac{1}{2} (m) \left ( v\right )^{2} = \frac{1}{2} mv^{2}

Option c) Kinetic energy after the collision:

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

Option d) Kinetic energy after the collision:

\\K_{a}=\frac{1}{2}mv^2+\frac{1}{2}m(\frac{v}{2})^2+\frac{1}{2}m(\frac{v}{3})^2\\\\=\frac{49}{72}mv^2

Hence, option b is correct.

Posted by

infoexpert24

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