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Question

Two bodies with kinetic energies in the ratio 4:1 are moving with equal linear momentum. The ratio of their masses is?


A

1:2

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B

1:1

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C

4:1

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D

1:4

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Solution

The correct option is C

4:1


Step 1: Given data

The ratio of two bodies with kinetic energies is = 4:1

We have to find the ratio of their mass.

Step 2: Formula to be used

The energy of a body due to its motion is known as kinetic energy.

The kinetic energy is,

K=mv22

Here m is the mass of the body and v is velocity.

We know that, if a body or object is at rest condition, then its velocity will be zero and since, zero kinetic energy.

The relation of momentum of body is,

p=mv

Where p is momentum, m is mass and v is the velocity.

Step 3: Finding the ratio of masses
The relation between the momentum and kinetic energy is given by

K=p22m
From the given,

K1K2=41

and also the linear momentum is the same for both bodies.

So,

K1K2=41

K1K2=p12×2m22m1×p22

p12×2m22m1×p22=41

m2m1=41

The ratio of their masses is = 4:1

Hence, option (C) is the correct answer.


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