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Question

A light and a heavy object have the same momentum. Find out the ratio of their kinetic energies. Which one has a larger kinetic energy?


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Solution

Step 1. Given data

The momentum of the light object and heavy object is the same.

Step 2. Formula used

  1. Momentum =mv
  2. Kinetic EnergyK.E=12mv2

Where m is the mass and v is the velocity of the object.

Step 3. Calculate the ratio of their kinetic energies

Let m is the mass and v is the velocity of the lighter object and M is the mass and V is the velocity of the heavy object.

Since both have the same momentum

mv=MVMm=vV

Clearly v>V

The kinetic energy of the lighter object will be be

K.E1=12mv2

The kinetic energy of the heavier object will be

K.E2=12MV2

K.E1:K.E2=12mv2:12MV2=mv2:mvVV2mM=Vv=v:V

So the ratio of the kinetic energy is v:V.

Step 4. Find the larger kinetic energy

v>V

So K.E1>K.E2

Hence, the ratio of the kinetic energies is v:V and the kinetic energy of the lighter object is greater than the kinetic energy of the heavier object.


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