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Question
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?
Options
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Solution
Explanation:
In a collision, if the motion of colliding particles before and after the collision is along the same line, the collision is said to be head-on or one-dimensional.
When two bodies of equal masses collide elastically, their velocities are interchanged.
Kinetic energy and linear momentum remain conserved Total kinetic energy of the system before the collision
= `1/2 mv^2 + 0 = 1/2 mv^2`
In (a), kinetic energy of the system after the collision.
`k_1 = 1/2 (2m) (v/2)^2 = 1/4 mv^2`
Hence this option is incorrect.
In (b), kinetic energy of the system after the collision.
`k_2 = 1/2 (m) (v)^2 = 1/2 mv^2`
Hence this option will be correct.
In (c), kinetic energy of the system after the collision.
`k_3 = 1/2 (3m) (v/3)^2 = 1/6 mv^2`
Hence this option is incorrect.
In (d), kinetic energy of the system after the collision.
`k_4 = 1/2 mv^2 + 1/2 m (v/2)^2 + 1/2 m(v/3)^2 = 49/72 mv^2`
We see that kinetic energy is conserved only in (b).
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