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If KE of a body increases by 300%, by wh...

If KE of a body increases by `300%`, by what `%` will the linear momentum of the body increase?

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Consider a particle of mass m moving with a velocity v. Its KE = `1/2 m v^2` and momentum, p = mv.
Thus, `KE = (p^2)/(2m) or p = sqrt(2m KE)`
When KE is increased by 300%, then new KE
`KE' = KE + 3KE = 4KE`
New momentum, `p' = sqrt(2m KE') = sqrt(2m xx 4 KE) = sqrt(8m KE) = 2p`
Percentage increase in momentum = `(p' - p)/(p) xx 100 = (2p-p)/(p) xx 100 = 100%`.
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