Question

Which of the following graphs can represent the relation between momentum (P) and kinetic energy (K) for a body in motion?

• A.
  
• B.
  
  
• C.
  
• D. None of these

Answer 1

Answer: (A)

As we know that,

$K=\frac{p^2}{2m}$

$lnK=2lnp-ln2m$

$2lnp=lnK+ln2m$

$lnp=\frac{1}{2}lnK+\frac{1}{2}ln2m$

Comparing with standard equation of straight line y=mx+c

$y=lnp$

$m=\frac{1}{2}$

$c=\frac{1}{2}ln2m$

Therefore it is a straight line with positive slope and positive y-intercept.

Hence, Option A is correct.