Since for a particle the kinetic energy is given by and

Solution 10DQ Introduction We have to discuss why kinetic energy changes while keeping momentum constant. Step 1 This is possible because the kinetic energy is not linear function of momentum rather it is the quadratic function. We can divide in two or more parts keeping the momentum same, that is suppose P is the initial momentum then we can divide it in n parts in such a way that P = P +1P + 2... + P n But so the total momentum will remain same. But in general the sum of the squares of the components will not be equal to the sum of the initial momentum , that is 2 2 2 2 P = / P 1 + P 2 + .... +nP So the kinetic energy can be different even if the total momentum remains same because the kinetic energy is a not a linear function of momentum.