Question

Two particles of masses m, and m, have
equal kinetic energies. The ratio of the
magnitude of their momentum is
(a) m^1:m₂
(b) m^2:m^1

(c) mm (d) mm​

Answer 1

Answer:

Linear momentum=mass×velocity

velocity of 1st body=v

1

kinetic energy of first body =

2m

1

p

2

=

2m

1

(m

1

v

1

)

2

velocity of 2nd body=v

2

kinetic energy of 2nd body=

2m

2

p

2

=

2m

2

(m

2

v

2

)

2

⇒

2m

1

(m

1

v

1

)

2

=

2m

2

(m

2

v

2

)

2

⇒

m

2

v

2

(m

1

v

1

)

=

(2m

1

)

(2m

2

)

=

2m

2

:

2m

1

Answer 2

Explanation:

Given,

Two bodies m1 and m2

Let the velocity of 1st body be = v1

Then its Kinetic energy = p²/2m1=(m1v1)²/2m2

Let the velocity of 2nd body be = v2

Then its Kinetic energy = p²/2m2 = (m2v2)²/2m2

Now, (m1v1)²/2m1 = (m2v2)²/2m2

∴(m1v1)/(m2v2) =  

Then Ratio = √(2m2) : √(2m1)

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