If you want to double the momentum of a gas molecule, by what factor must you increase its kinetic energy?
A) 2
B) 4
C) $2 \sqrt { 2 }$
D) $\sqrt { 2 }$
E) 16

Question

If you want to double the momentum of a gas molecule, by what factor must you increase its kinetic energy? 
A) 2
B) 4
C) $2 \sqrt { 2 }$
D) $\sqrt { 2 }$
E) 16

Quizplus · Accepted Answer

Momentum $ p $ is given by $ p = mv $, and kinetic energy $ KE $ is given by $ KE = \frac{1}{2}mv^2 $. If momentum is doubled, $ 2p = 2mv $, which implies velocity $ v $ is doubled. Substituting $ 2v $ into the kinetic energy equation gives $ KE' = \frac{1}{2}m(2v)^2 = 4 \times \frac{1}{2}mv^2 = 4KE $. Thus, kinetic energy must be increased by a factor of 4.

If You Want to Double the Momentum of a Gas 222 \sqrt { 2 }22​

If You Want to Double the Momentum of a Gas $2 \sqrt { 2 }$