Momentum of a body is doubled. By what percentage does the Kinetic energy of the body change?

Sure, let's solve this step by step.

Step 1: Understand the relationship between momentum and kinetic energy. The formula for kinetic energy (K.E) is (1/2)mv^2 and the formula for momentum (p) is mv.

Step 2: From the above formulas, we can express v (velocity) in terms of momentum and mass: v = p/m.

Step 3: Substitute v in the kinetic energy formula: K.E = (1/2)m(p/m)^2 = p^2/2m.

Step 4: If the momentum is doubled, the new kinetic energy (K.E') will be ((2p)^2)/(2m) = 4p^2/2m = 2p^2/m.

Step 5: The change in kinetic energy is K.E' - K.E = 2p^2/m - p^2/2m = p^2/2m.

Step 6: To find the percentage change, divide the change in kinetic energy by the original kinetic energy and multiply by 100: (p^2/2m) / (p^2/2m) * 100 = 100%.

So, the kinetic energy of the body changes by 100% when the momentum is doubled.