two bodies of mass 10 kg and 40 kg respectively have the same kinetic energy. Find the ratio of their momentum
Answers
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:
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 =
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,
10 = 40
= 40/10
= 4/1
Now, we are going to take square root on both sides, we get,
=
= 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 =
p1/p2 =
p1/p2 =
p1/p2 =10/40*2/1
p1/p2 = 0.2* 2
p1/p2 =1/2
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