Question

A light and a hevay body have equal momenta.tge light body is greater K.E ,why?

Answer 1

Let the velocities of lighter and heavier elements be v and V with masses as m and M.

Momentum of lighter particle = mv

Momentum of heavier particle = MV

Given , m < M

           mv = MV

This can only happen when v > V .

Verification :

m = 1 kg and M = 2 kg

For mv = MV

v = 2 m/s and V = 1 m/s ( isn't it )

Here also v > V

For kinetic energy

For lighter body to have  higher K.E

i.e $\frac{1}{2} mv^{2} > \frac{1}{2} MV^{2}$

This is so because v > V

                            ⇒  $v^{2}  > V^{2}$      [ squaring both side won't                

                                                                               change the sign as both

                                                                                velocities are positive ]

Verification

m = 1 kg , M =2 kg

v = 2 m/s, V = 1 m/s

K.E ₁ = $\frac{1}{2} mv^{2}$

        = $\frac{1}{2} . 1. 2^{2}$

        = 2 Kg-m²/s²

K.E₂ = $\frac{1}{2}MV^{2}$

       =$\frac{1}{2}  . 2 .1^{2}$

       = 1  Kg-m²/s²

Here K.E ₁ > K.E ₂    as  v² > V² .

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