Question

The kinetic energy of a body of mass m is E. Its momentum is: *
a) √2mE
b) 2mE
c) √(mE/2)
d) 2E/m

Answer 1

Answer:

Given:

Mass of body = m

Kinetic Energy is E

Momentum be p

To find:

Relationship between Kinetic energy and Momentum.

Concept:

We know that :

$kinetic \: energy = \frac{1}{2} m {v}^{2}$

$= > E= \dfrac{1}{2} m {v}^{2}$

$= > E= \dfrac{1}{2} m { \bigg(\dfrac{p}{m} \bigg) }^{2}$

$= > E= \dfrac{ {p}^{2} }{2m}$

$= > {p}^{2} = 2mE$

$= > p = \sqrt{2mE}$

So final answer :

$\boxed{ \red{ \sf{ \huge{ \bold{ p = \sqrt{2mE} }}}}}$

Additional information:

• Momentum is an index of the inertia of the body. It is given as the product of mass and acceleration.
• Kinetic energy is the amount of energy present in a body by the virtue of it's motion only.
• Kinetic energy is scalar Quantity, but momentum is vector.
• Scalars just have magnitude and no directions. But vectors have both.