Question

2 if the mass of a body is m and its kinetic energy is E Prove that the momentum of the body is equal to (2mE)1 /2

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Answer 1

Answer:

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} }(2mE)

2

1

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} }mass×velocity=(2mE)

2

1

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

2

1

Hence, given expression for momentum is proved.