Question

If the mass of body is m and its kinetic is E,prove that the moment of the body is equal to (2mE)^1/2

Answer 1

Answer:

Given,

Mass of the body = m

Kinetic energy = E

To find,

To show that the momentum of the body is equal to

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

2

1

Solution,

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

As, there is certain amount of kinetic energy in the said body. So, the body has to possess certain amount of motion, as well as velocity.

Let, the velocity of the body = v

Now, we know that

Kinetic energy = ½ × mass × (velocity)² = ½×m×v² = ½mv²

Acording to the data mentioned in the question,

E = ½mv²

½mv² = E

mv² = 2E

m²v² = 2mE [Multiplying both sides with the mass of the body.]

√(m²v²) = √(2mE)

mv = √(2mE)

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

2

1

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

2

1

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

2

1

Hence, the given expression for momentum is proved.

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