If the speed of a moving particle is tripled, then the ratio of its kinetic energy to its momentum will be

1. doubled
2. tripled
3. quadrupled
4. None of these

tripled

Reason — Let velocity be v then

Kinetic energy (KE) = $\dfrac{1}{2}mv^2$ and

momentum (ρ) = mv

$\dfrac{KE}{ρ} = \dfrac{\dfrac{1}{2}mv^2}{mv} = \dfrac{v}{2}$    [Equation 1]

Now, when velocity is tripled then

KE' = $\dfrac{1}{2}m(3v)^2$ = $\dfrac{9}{2}m(v)^2$

and ρ' = 3mv

$\dfrac{KE'}{ρ'} = \dfrac{\dfrac{9}{2}mv^2}{3mv} = \dfrac{3v}{2}$    [Equation 2]

On comparing equation 1 and 2, we can see that the ratio gets tripled.