Question

if the mass of a body is m and it's kinetic energy is e prove that the momentum of the body is equal to (2mE )1/2 ​

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 :

So final answer :

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.

Explanation:

Answer 2

Given,

Mass of the given body = m

Kinetic energy of the given body = E

To find,

To show that the momentum of the body is :

${(2mE)}^{ \frac{1}{2} }$

Solution,

We can simply solve this numerical problem by using the following process.

Now, existence of kinetic energy means the body is in motion.

Let, the velocity of the body = v

Here, we will need the mathematical expression of Kinetic energy of a body.

Kinetic energy = ½ × mass × (velocity)²

By, putting the given values,

Kinetic energy = ½ × m × v² = mv²/2

According to the data mentioned in the question,

E = mv²/2

2E = mv²

2mE = m²v² [Multiplying both sides with mass (m).]

m²v² = 2mE

mv = √(2mE)

$mass \times velocity = {(2mE)}^{ \frac{1}{2} }$

$momentum = {(2mE)}^{ \frac{1}{2} }$

Hence, given expression for momentum is proved.