A rock is moving with speed v.If the mass of the rock were tripled and the speed were reduced to v/3,which of the following statements would be true?
A)The kinetic energy of the rock is smaller than in the first case,but the momentum is larger.
B)The kinetic energy of the rock is smaller than in the first case,but the momenta of both are the same.
C)The kinetic energies of the rocks are the same in both cases.
D)The kinetic energy of the rock is 1/9 its previous value.

Question

Quizplus · Accepted Answer

The kinetic energy (KE) is given by $KE = \frac{1}{2}mv^2$, and the momentum (p) is given by $p = mv$. Initially, let's denote the mass as $m$ and the velocity as $v$. In the second scenario, the mass is tripled to $3m$ and the velocity is reduced to $v/3$. The kinetic energy in the first case is $KE_1 = \frac{1}{2}mv^2$, and in the second case, it is $KE_2 = \frac{1}{2}(3m)(v/3)^2 = \frac{1}{2}mv^2/3$, showing that the kinetic energy is indeed smaller in the second case. The momentum in the first case is $p_1 = mv$, and in the second case, it is $p_2 = 3m(v/3) = mv$, showing that the momenta are the same in both cases.

A Rock Is Moving with Speed V