Question

Two bodies of masses 2m and m have their kinetic energy in the ratio 8:1 , then the ratio of their linear momenta is
a) 1:4
b) 1:8
c) 8:1
d)4:1​

Answer 1

Answer :-

Ratio of linear momenta of the bodies is 4 : 1 [Option.d]

Explanation :-

We have :-

→ Mass of 1st body = 2m

→ Mass of 2nd body = m

→ Ratio of Kinetic energy = 8 : 1

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Let the Kinetic energy of the 1st body be 8x and the second body be x .

Also, let momentum of the 1st body be p₁ and the 2nd body be p₂ .

For the 1st body :-

⇒ p² = 2 × m × K.E.

⇒ p²₁ = 2 × 2m × 8x

⇒ p²₁ = 32mx ---(1)

For the 2nd body :-

⇒ p²₂ = 2 × m × x

⇒ p²₂ = 2mx ---(2)

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On dividing eq.1 by eq.2, we get :-

⇒ p²₁/p²₂ = 32mx/2mx

⇒ p²₁/p²₂ = 16/1

⇒ √(p²₁/p²₂) = √(16/1)

⇒ p₁/p₂ = 4/1

⇒ p₁ : p₂ = 4 : 1

Answer 2

Given :-

Two bodies of masses 2m and m have their kinetic energy in the ratio 8:1

To Find :-

then the ratio of their linear momenta is

Solution :-

We know that

p = √2mKE

Where

p = linear moment

m = mass

KE = Kinetic energy

p/p' = √(2(2m)KE)/√(2mKE)

p/p' = √(4m × 8)/√(2m × 1)

p/p' = √(32m/2m)

p/p' = √(16/1)

p/p' = 4/1

p : p' = 4 : 1

Hence

The ratio is 4 : 1