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Question

Two masses of 1g and 4g are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is


A

4 : 1

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B

2:1

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C

1 : 2

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D

1 : 16

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Solution

The correct option is C

1 : 2


Step-1: Given data:

Let the first mass be m1=m

Let the second mass be m2=4m

Kinetic energy of first mass = Kinetic energy of second mass = K.E.

Velocity of first mass = V1

Velocity of second mass = V2

Step 2: Formula Used

Kinetic energy of a particle with mass m and velocity v is given by: K.E.=12mv2

Linear momentum of a particle of mass m and velocity V is given by: p=mV

Step-3: Calculation:

We have two cases as the Kinetic energy is equal for both cases.

K.E.=12mV12...........(i)

K.E.=12(4m)V22............(ii)

Dividing equation (i) with (ii) we get,

V1=2V2

Now we have,

P1=m1V1 and P2=m2V2

Dividing P2byP1 we get

P2P1=m2V2m1V1

P2P1=mV1m2V2

P2P1=12

The ratio of the magnitudes of their linear momenta is 12

Therefore, option (C) is the correct answer.


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