If the kinetic energy of a body is increased by 300%, its momentum will increase by

The kinetic energy (KE) of an object is given by the formula KE = 1/2 mv^2, where m is the mass and v is the velocity of the object.

The momentum (p) of an object is given by the formula p = mv.

If the kinetic energy is increased by 300%, it means the kinetic energy is multiplied by 4 (since the original kinetic energy is 100%, and 300% increase makes it 400%).

Let's denote the initial velocity as v1 and the final velocity (after the increase in kinetic energy) as v2. We have:

1/2 m v1^2 = KE (initial kinetic energy) 1/2 m v2^2 = 4 * KE (final kinetic energy)

From these equations, we can derive that v2^2 = 4 * v1^2, which means v2 = 2 * v1.

Now, let's calculate the increase in momentum. The initial momentum is p1 = m * v1, and the final momentum is p2 = m * v2 = m * 2 * v1 = 2 * p1.

So, the momentum is increased by 100%.