Q8. The momentum of a body is double. By what percentage does it its kinetic energy increases?

 

Asked by sbidipak | 5th Jul, 2017, 07:33: PM

Expert Answer:

begin mathsize 12px style The space relation space between space KE space and space momentum space is space
KE space equals space fraction numerator straight p squared over denominator 2 straight m end fraction
So space KE space is space directly space proportional space to space the space square space of space the space momentum.
So space taking space the space ratios space we space get
fraction numerator KE subscript 1 over denominator straight p subscript 1 superscript 2 end fraction equals fraction numerator KE subscript 1 over denominator straight p subscript 2 superscript 2 end fraction
But space straight p subscript 2 space equals space 2 straight p subscript 1
rightwards arrow fraction numerator KE subscript 1 over denominator straight p subscript 1 superscript 2 end fraction equals fraction numerator KE subscript 2 over denominator 4 straight p subscript 1 superscript 2 end fraction
therefore KE subscript 2 space equals space 4 KE subscript 1
Thus comma space KE space will space increase space by space straight a space factor space of space 4. end style

Answered by Yashvanti Jain | 6th Jul, 2017, 10:42: AM

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