For the Same Kinetic Energy of a Body, What Should Be the Change in Its Velocity If Its Mass is Increased Nine Times?

For the same kinetic energy of a body, what should be the change in its velocity if its mass is increased nine times?

Numerical

Let initial mass m₁ = m, initial velocity v₁ = v

Final mass m₂ = 4m, Find velocity = v₂

For the same kinetic energy,

`1/2`m₁v₁² = `1/2` m₂v₂² or `1/2` mv² =`1/2` × 9m × v₂²

v2 =`sqrt(1/9"v"^2)=1/3"v".`

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