Saturday, August 18, 2018

Two bodies of masses m1 and me have equal kinetic energies. What is the ratio of their linear momentum

k i n e t i c space e n e r g y equals K. E equals 1 half m v squared w e space k n o w space t h a t space m o m e n t u m equals p equals m v K. E equals 1 half m v squared equals 1 half cross times m v cross times v equals 1 half cross times m v cross times fraction numerator m v over denominator m end fraction equals fraction numerator p squared over denominator 2 m end fraction K. E equals fraction numerator p squared over denominator 2 m end fraction f o r space m a s s space m subscript 1 left parenthesis K. E right parenthesis subscript 1 equals fraction numerator p subscript 1 squared over denominator 2 m subscript 1 end fraction......... left parenthesis 1 right parenthesis f o r space m a s s space m subscript 2 left parenthesis K. E right parenthesis subscript 2 equals fraction numerator p subscript 2 squared over denominator 2 m subscript 2 end fraction............ left parenthesis 2 right parenthesis h e r e comma space left parenthesis K. E right parenthesis subscript 1 equals space left parenthesis K. E right parenthesis subscript 2 space space space space space space space space space space space space space space space space fraction numerator p subscript 1 squared over denominator 2 m subscript 1 end fraction equals fraction numerator p subscript 2 squared over denominator 2 m subscript 2 end fraction space space space space space space space space space space space space space space space p squared subscript 1 over p squared subscript 2 equals fraction numerator 2 m subscript 1 over denominator 2 m subscript 2 end fraction space space space space space space p subscript 1 over p subscript 2 equals square root of m subscript 1 over m subscript 2 end root r a t i o space o f space t h e i r space l i n e a r space m o m e n t u m equals square root of m subscript 1 over m subscript 2 end root
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