Question

Two bodies have ratio of their masses m1/m2=1:4 and ratio of their kinetic energies ,
KE1/KE2=9 .The ratio of their velocities v1/v2 is

Answer 1

Given :

Ratio of the masses of two bodies, m₁ : m₂ = 1 : 4

Ratio of their kinetic energies, KE₁ : KE₂ = 9

To find :

Ratio of their velocities, v₁ : v₂

Solution :

∵ Kinetic energy, KE = 1/2 mv²

Now putting values,

⇒ KE₁/KE₂ = (1/2 m₁v₁²)/(1/2 m₂v₂²)

⇒ 9 = (1/2 × 1 × v₁²)/(1/2 × 4 × v₂²)

⇒ 9 = (1/2 v₁²)/(2 v₂²)

⇒ 9 = v₁²/4v₂²

⇒ √9 = √(v₁²/4v₂²)

⇒ 3 = v₁/2v₂

⇒ v₁ = 6v₂

⇒ v₁/v₂ = 6/1

⇒ v₁ : v₂ = 6 : 1

∴ Ratio of their velocities, v₁ : v₂ = 6 : 1

Answer 2

$\bf Required\: Answer \: is \: as \: follows$

As we know that

Kinetic energy = ½mv²

M is the Mass

V is the Velocity

Let the two body be

KE/KE' = ½mv²/½m'v'²

9 = ½ × 2 × v²/½ × 4 × v'²

9 = 1 × v²/½ × 4 × v'²

9 = 1 × v²/2 × v'²

√9 = √v²/4v'²

3 = √v/4v'

3 = v/2v'

2 × 3 = v/v'

v/v' = 6:1

Therefore :-

Ratio between velocities of v/v' is 6:1