Question

the masses of a lighter and heavier body are m and M respectively if they have the same momentum determine which one has a greater kinetic energy

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Answer 1

Explanation:

Lighter object will have greater kinetic energy. This is because if both the lighter and heavier objects have the same momentum then it is clear that lighter object will have the greater velocity and since kinetic energy is velocity dominant so the lighter object with higher velocity will have higher kinetic energy

Let m

1

and m

2

be the masses of the body

Let m

1

>m

2

Given that

m

1

v

1

=m

2

v

2

v

2

v

1

=

m

1

m

2

∴ Ratio between their kinetic energies , =

K

2

K

1

=

2

1

m

2

v

2

2

2

1

m

1

v

1

2

⟹

K

2

K

1

=

m

2

m

1

×

m

1

2

m

2

2

=

m

1

m

2

This shows the Kinetic energy is greater for that mass which is lighter

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