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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. If the Collision is Elastic, Which of the Following Figure is a Possible Result After Collision - CBSE (Science) Class 11 - Physics

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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. If the collision is elastic, which of the following figure is a possible result after collision?

Solution 1

Let m be the mass of each ball bearing. Before collision, total K.E. of the system

=1/2mv2 + 0 =1/2 mv2

After collision, K.E. of the system is

Case I, E1 = 1/2 (2m) (v/2)2 = 1/4 mv2

Case II, E2 = 1/2 mv2

Case III, E3 = 1/2(3m) (v/3)2 = 1/6mv2

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

Solution 2

It can be observed that the total momentum before and after collision in each case is constant.

For an elastic collision, the total kinetic energy of a system remains conserved before and after collision.

For mass of each ball bearing m, we can write:

Total kinetic energy of the system before collision:

= (1/2)mV2 + (1/2)(2m) × 02

= (1/2)mV2

Case (i) 
Total kinetic energy of the system after collision:

= (1/2) m × 0 + (1/2) (2m) (V/2)2

= (1/4)mV2

Hence, the kinetic energy of the system is not conserved in case (i).

Case (ii)
Total kinetic energy of the system after collision:

= (1/2)(2m) × 0 + (1/2)mV2 

= (1/2) mV2

Hence, the kinetic energy of the system is conserved in case (ii).

Case (iii)

Total kinetic energy of the system after collision:

= (1/2)(3m)(V/3)2

= (1/6)mV2

Hence, the kinetic energy of the system is not conserved in case (iii). 

Hence, Case II is the only possibility.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Physics Textbook for Class 11 (2018 to Current)
Chapter 6: Work, Energy and Power
Q: 16 | Page no. 136
Solution 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 Possible Result After Collision Concept: Concept of Collisions.
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