Question

A body of m is moving in a straight line at a constant speed v. Its kinetic energy is k and the magnitude of its momentum is p. Which of the following relations is/are correct?

• A. $2k=pv$
• B. $p=\sqrt{2mk}$
• C. $v=\sqrt{\frac{2k}{p}}$
• D. $p=\sqrt{\frac{2k}{m}}$

Answer 1

Answer: (A), (B)

$p=\sqrt{2mk}$

Now p=mv or $p^2=m^2{v}^2$ or $\frac{p^2}{2m}=\frac{1}{2}m{v}^2=k$ or $p=\sqrt{2mk}$. Also p = mv and $k=\frac{1}{2}m{v}^2$. Dividing the two we get 2k = pv. Hence the correct relations are (a) and (c).