Answer to Question #106373 in Mechanics | Relativity for Valentine Agun

Question

. If two particles have equal momenta, are their kinetic ener- gies equal? (a) yes, always (b) no, never (c) no, except when their masses are equal (d) no, except when their speeds are the same (e) yes, as long as they move along parallel lines.

Answer 1

As per the given question,

Two particles have the same momentum, then we have to find that their energy will be same or not ?

let the masses of the objects are m1 and m2 and their velocities are V1 and V2

As per the question,

momentum of the both particles are same, so

$m_1 V_1 = m_2 V_2$

Now, energy of the first = $\dfrac{m_1V_1^2}{2}$

energy of the second particle =$\dfrac{m_2 V_2^2}{2}$

Now, from that above, we can say that It will not be equal,

If both the particles will have the same mass and same velocity then their energy will be same.

Since, momenta of heavy body and light body are same, thus velocity of light body is greater than that of heavy body. Also, kinetic energy is proportional to the square of velocity hence, lighter body has greater kinetic energy.

so c is the correct answer.