Question

the kinetic energy k depends upon momentum p and mass m the correct relation may be a) k=p^2/2m b)k= 1/2p^2m c)k=1/2pm d) k=1/2pm^2


with proof please ​

Answer 1

Given info : the kinetic energy K depends upon momentum p and mass m.

To find : the correct relation may be ..

solution : kinetic energy of a body is given by , K = $\frac{1}{2}mv^2$

$\implies \frac{2K}{m}=v^2$  ...(1)

and momentum of the same body is given by, P = mv

⇒ P² = m²v²

⇒ $P^2=m^2\times\frac{2K}{m}$  [ from equation (1) ]

⇒ P² = 2Km

⇒ $K=\frac{P^2}{2m}$

therefore the correct relation between them is $K=\frac{P^2}{2m}$ . i.e., the correct option is (a) $K=\frac{P^2}{2m}$