Question

two bodies of mass 10 kg and 40 kg respectively have the same kinetic energy. Find the ratio of their momentum

Answer 1

Concept:

Kinetic energy of a body:

K.E. = (1/2)mv²

where m, and v is the mass and velocity of the body respectively.

Given :

Mass of the 1st body, m₁ = 10 kg

Mass of the 2nd body, m₂ = 40 kg

The kinetic energy of both the bodies is equal.

Find :

The ratio of momentum of the given two bodies.

Solution:

For body A, let the mass and velocity of the body be m₁ and v₁.

Similarly, for body B, let the mass and velocity of the body be m₂ and v₂.

Given,

K.E.₁ = K.E.₂

(1/2)m₁v₁² =(1/2)m₂v₂²

10v₁² = 40v₂²

v₁²/v₂² = 40/10

(v₁/v₂)² = 4/1

Taking square root on both sides,

v₁/v₂ = √4/1

v₁/v₂ = 2/1

The momentum of a body can be defined as, p = mv

where m and v is the mass and velocity of the body respectively.

We have to calculate p₁ : p₂

p₁ : p₂ = m₁v₁ : m₂v₂

p₁/p₂ = m₁v₁/m₂v₂

p₁/p₂ = m₁/m₂ × v₁/v₂

p₁/p₂ = 10/40 × 2/1 ⠀⠀

p₁/p₂ = 1/2

Hence, the ratio of the momentum of the given two bodies is 1 : 2.

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Answer 2

Answer:

The ratio of their momentum is 1/2.

Explanation:

• A kinetic energy is the process of energy of a motion, that will observe the movement of any particle or the sets of the particle.
• Let us consider the following as object that is moving in a motion using the method of kinetic energy:

When a base ball is thrown.

A charge of the particle in the electric field.

There are five types of Kinetic Energy:

1) Radiant

2) Thermal

3) sound

4) Mechanical

5) Electrical

• The SI unit of kinetic energy is joule.
• The formula for the kinetic energy is:

KE =$1/2mv^{2}$

Given that:

The two bodies of mass 10 kg and 40 kg respectively have the same kinetic energy.

To find:

the ratio of their momentum =?

Solution:

Let us consider,

The mass and velocity of the body to be m1 and v1

The mass and velocity of body B to be m2 and v2.

Now, let us consider it by applying the formula of Kinetic energy, we get,

$K.E_{1} = K.E_{2}$

$(1/2) m_{1} v_{1} ^{2} = (1/2) m_{2} v_{1} ^{2}$

10 $v_{1} ^{2}$ = 40 $v_{2} ^{2}$

$v_{1} ^{2} / v_{2} ^{2}$ = 40/10

$(v_{1} / v_{2} )^{2}$ = 4/1

Now, we are going to take square root on both sides, we get,

$v_{1} / v_{2} ^{2}$ = $\sqrt{4/1}$

$v_{1} / v_{2}$ = 2/1

Therefore, the momentum of the body is p=mv

Here, m and v is mass and velocity of the body.

Now, we are going to calculate the ratio of p1: p2

p1:p2 =$m_{1} v_{1} :m_{2} v_{2}$

p1/p2 = $m_{1} v_{1} /m_{2} v_{2}$

p1/p2 = $m_{1} v_{1} / m_{2} v_{2}$

p1/p2 =10/40*2/1

p1/p2 = 0.2* 2

p1/p2 =1/2

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