a light and a heavy body have same Momentum which one has larger kinetic energy
Answers
e: Considering the situation in space/vacuum.
Momentum is the product of Mass of the body and its Velocity!
Kinetic energy is the product of Mass and the square of the velocity!
We can also write Kinetic energy as the product of the momentum and the velocity!
K.E=M.v
Where, K.E is kinetic energy,
M is mass of the body
v is velocity of the body.
Say, a light body having a mass 'm1' and a velocity 'v1'
&
a heavy body having a mass 'm2' and a velocity 'v2'
And their momentums be M.
As we know that for a constant momentum, mass and velocity are inversely proportional to each other, here light body(having less mass) will have more velocity(v1) compared to heavy body's(having more mass). So, v1>>v2
As the question conditions that both the bodies has same momentum, say M.
Now, the Kinetic energy of both the bodies will be
K.E1 = m1.(v1)²/2 & K.E2 = m2.(v2)²/2
We can also write Kinetic energy as the product of momentum and Velocity, K.E=m.v²/2 => K.E=m.v.v/2 => (m.v).(v/2) => M.(v/2)
As we have momentums same here, we can substitute M in kinetic energy equations..
K.E1 = M.v1/2 & K.E2 = M.v2/2
As v1 is greater than v2
Hence K.E1 will have more kinetic energy, which means light body will have more kinetic energy than the heavy body!
P.S: Sorry for being lengthy. I have tried my own way. Wish I could explain in a fluent manner!