Correct Answer - Option 2 : comes to rest after collision
The correct answer is option 2) i.e. comes to rest after the collision
CONCEPT:
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Elastic collision: Elastic collision is a phenomenon where the collision of objects takes place such that the total linear momentum and kinetic energy of the system are conserved.
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Law of conservation of momentum: Momentum is conserved for any interaction between objects in an isolated system, provided there are no external forces.
- The conservation of momentum can be observed by analyzing the momentum of the total system or by analyzing the change in momentum.
- This is done by equating the momentum before the interaction to the momentum after the interaction.
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Kinetic energy is the energy possessed by a moving object.
Kinetic energy (KE) is expressed as:
\(KE =\frac{1}{2} mv^2\)
Where m is the mass of the object and v is the velocity of the object.
EXPLANATION:
Let m be the mass of the two identical balls.
u1 = velocity before the collision of ball 1
u2 = 0 = velocity of second ball that is at rest
v1 and v2 are the velocities of the balls after the collision.
From the conservation of momentum,
mu1 + mu2 = mv1 + mv2
⇒ mu1 = mv1 + mv2 ⇒ u1 = v1 + v2
In an elastic collision, the kinetic energy of the system before and after collision remains same.
\(\frac{1}{2}mu_1^2 + 0 = \frac{1}{2}mv_1^2 + \frac{1}{2}mv_2^2\)
\(⇒ \frac{1}{2}m(v_1 + v_2)^2 = \frac{1}{2}mv_1^2 + \frac{1}{2}mv_2^2\)
\(⇒\frac{1}{2}mv_1^2 + \frac{1}{2}mv_2^2 + mv_1v_2 = \frac{1}{2}mv_1^2 + \frac{1}{2}mv_2^2\) ⇒ mv1v2 = 0
- The mass cannot be zero.
- The second ball moves, hence velocity v2 cannot be zero.
- Thus, the velocity of the first ball v1 is zero i.e. it comes to rest after collision.
