Two body of mass m1 and m2 have equal kinetic energy posses greater inner momentum
Answers
Two masses M1 and M2 have equal kinetic energy. Which mass will have greater momentum?
Here, in the context of the question in which word 'greater ' has been used, there is no need of consider mass and kinetic energy as scalar and momentum as vector. We have been asked to compare the magnitudes of momenta.
Also, the relation between mass, kinetic energy and momentum is in scalar form as momentum square is appearing in that relation:
Kinetic energy K= p^2/(2m)
K1=p1^2/(2M1)=p2^2/2M2)=K2.( Because kinetic energies are given equal.)
p1/p2=sqrt(M2/M1).
If M2>M1 ,suppose, then
p1>p2.
Now, in some answers relativity has been brought in picture. For this we have to assume velocities in relativistic region.
In that case,kinetic energy = mc^2=( cp)^2- (moc^2)^2.
For equal kinetic energy,
(cp1)^2- (M1c^2)^2 =(cp2)^2-(M2c^2)^2.
Or
(cp1)^2-(cp2)^2=(M1c^2)^2-(M2c^2)^2. So,if
M2>M1,
p2>p1.
This result differs from non relativistic result!!
Remember that the questioner has not mentioned M1 and M2 as rest masses.