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Question

Two bodies of masses m and 4m are moving with equal linear momenta. The ratio of their kinetic energies is


A

1:4

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B

4:1

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C

2:1

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D

1:2

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Solution

The correct option is B

4:1


Step 1. Given data

Mass of first body is given as m, mass of second body is given as 4m which are moving with equal linear momenta p1 and p2 as shown in above figure.

We have to find the ratio of kinetic energy.

Step 2. Formula to be used

Only moving objects can possess kinetic energy and momentum. If we adapt the mass time squared velocity definition, kinetic energy and momentum are related to one another and we will get,

E=p22m

Here, p is momentum, m is the mass and E is energy.

Step 3. Find the ratio of kinetic energy.

Let,

p1=2mK.E1

p2=2×4mK.E2

=8mK.E2

If p1=p2 for two bodies, we get,

2mK.E1=8mK.E2

Squaring on both sides.

2mK.E12=8mK.E22

2mK.E1=8mK.E2

2mK.E18mK.E2=1

14K.E1K.E2=1

K.E1K.E2=41

Therefore, the ratio of kinetic energies are 41.

Hence, option B is correct answer.


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