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ICSE Class 10 Answered

If 'm' is the mass of the body, 'v' its velocity and 'p' the momentum then write a relationship between change in momentum, mass and velocity of the body when: 1) v is almost equal to c, the velocity of light. 2) v is very very less as compared to c, the velocity of light.
Asked by kadtej83 | 26 Jun, 2019, 07:18: PM
answered-by-expert Expert Answer
Relativistic momentum p of a mass m moving with speed u is given by,  p = begin mathsize 14px style m fraction numerator u over denominator square root of 1 minus begin display style u squared over c squared end style end root end fraction end style ....................(1)
It is assumed, the speed u is very near to speed of light c, otherwise we get  p = m×u ...............................(2)
 
When a mass of m changing its speed u1 to u2 , if speeds are very near to speed of light,
then change in momentum ( p2 - p1 ) = begin mathsize 12px style m open square brackets fraction numerator u subscript 2 over denominator square root of 1 minus begin display style fraction numerator u subscript 2 superscript 2 over denominator c squared end fraction end style end root end fraction space minus space fraction numerator u subscript 1 over denominator square root of 1 space minus space begin display style fraction numerator u subscript 1 superscript 2 over denominator c squared end fraction end style end root end fraction close square brackets end style ................(3)
 
if speeds are very much less than speed of light, then ( p2 - p1 ) = m( u2 - u1 ) ......................(4)
 
Answered by Thiyagarajan K | 26 Jun, 2019, 10:58: PM

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