Question

Two bodies A and B have masses in the ratio 5:1 and their kinetic
energies are in the ratio 125:9. Find the ratio of their velocities.​

Answer 1

Answer:

Let mass of body A is

mass of body B is

a/c to question,

.....(1)

.

.......(2)

we know, formula of kinetic energy ,

or,

or,

or,

or,

or,

hence, ratio of their velocities is 5 : 3

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Guven,

Ratio of the mass of the body = 5 : 1`

Ratio of the Kinetic Energy of the body = 125/9

Since, K.E. = 1/2 mv²

Therefore, Ratio of K.E.₁ : K.E.₂ = m₁v₁²/m₂v₂²

∴ v₁²/v₂² = K.E.₁/K.E.₂ × m₂/m₁

∴ v₁²/v₂² = 125/9 × 1/5

∴ v₁²/v₂² = 25/9

∴ v₁/v₂ = 5/3

Hence, the ratio of the velocity of the body a to the velocity of the body b is 5 : 3.

Hope it helps.

Explanation:

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Answer 2

Correct question:-

Two bodies A and B have masses in the ratio 5:1 and their kinetic energies are in the ratio 125:9.Find the ratio of their velocities.

Given:-

•Ratio of masses(m1:m2)=5:1

•Ratio of Kinetic energies(K.E1:K.E2)=125:9

To find:-

•Ratio of their velocities

Solution:-

We know that:-

K.E=1/2mv²

=>K.E 1/K.E. 2 = (1/2m1v1²)/(1/2m2v2²)

=>K.E 1/K.E. 2= m1v1²/m2v2²

=>125/9 = m1v1²/m2v2²

=>125/9 =5/1(v1²/v2²)

=>v1²/v2²= 125/9×1/5

=>v1²/v2²= 25/9

=>v1/v2=5/3

=>v1:v2= 5:3

Thus,ratio of their velocities is 5:3.