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# Which would have a greater effect on the kinetic energy of an object: doubling the mass or doubling the velocity?

We know the formula for kinetic energy: $K=\frac{1}{2}mv^2$

Here, $K\rightarrow$kinetic energy of the moving body

$m\rightarrow$ mass of the body

$v\rightarrow$ velocity of the moving body

**On doubling the mass of the body:**

**
**

Mass will become $2m$

Then, kinetic energy of the body $K'=\frac{1}{2}\times(2m)\times v^2$

Or $K'=2\times\frac{1}{2}mv^2$

Or $K'=2K$

Thus, by doubling the mass of the body, the kinetic energy of the body will get doubled.

**On doubling the velocity of the body:**

**
**

On doubling the velocity, it becomes $2v$

Then kinetic energy of the body $K''=\frac{1}{2}m(2v)^2$

Or $K"=4\times\frac{1}{2}mv^2$

Or $K"=4K$

Thus, on doubling the velocity of the body, its kinetic energy becomes four times.

Therefore, doubling the velocity of the object has a greater effect on the kinetic energy of an object than doubling the mass of the object.