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" The graph between "sqrt(E(k))" and "1/...

" The graph between "sqrt(E_(k))" and "1/p" is (Ek=kinetic energy "p" = momentum) "

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Relation between kinetic energy and momentum Let us consider a body of mass 'm' having a velocity 'v', then momentum of the body P = mass xx velocity P = m xx v rArr v = (P)/(m) " "...(1) From definition, kinetic energy (K.E) of the body K.E = (1)/(2) mv^(2)" "...(2) Now putting the value of (1) in (2) we have K.E = (1)/(2)m ((P)/(m))^(2) K.E. = (1)/(2)m (P^(2))/(m^(2)) = (1)/(2) (P^(2))/(m) = (P^(2))/(2m)" "...(3) Thus we can write P^(2) = 2m xx K.E rArr P = sqrt(2m xx K.E) Thus momentum = sqrt(2 xx "mass" xx "kinetic energy") What will be the momentum of a body of mass 100 g having kinetic energy of 20 J ?

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(a) A proton is moving at a speed much less than the speed of light. It has kinetic energy K_1 and momentum p_1 . If the momentum of the proton is doubled, so p_2 = 2 p_1 , how is its new kinetic energy K_2 related to K-1 ? (b)A photon with energy E_1 has momentum p_1 . if another photon has momentum p_2 that is twice p_1 , how is the energy E_2 of the second photon related to E_1 ?