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Two particles of masses 2g and 4g have equal momentum. What is the ratio between their kinetic energies?
- a)2:1
- b)1:2
- c)1:3
- d)3:1
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Two particles of masses 2g and 4g have equal momentum. What is the rat...
Momentum is the product of mass and velocity. P =2×u, u= p/2. Again p =4×v, v = p/4. So, velocity of first
particle is twice the second. Ratio of kinetic energy = =(1/2×2×p/2×p/2) /(1/2×4×p/4×p/4)= 2/1 = 2:1.
Most Upvoted Answer
Two particles of masses 2g and 4g have equal momentum. What is the rat...
Ratio of kinetic energies: 2:1
Explanation:
To solve this problem, we need to understand the relationship between momentum and kinetic energy.
The momentum (p) of an object is defined as the product of its mass (m) and velocity (v). Mathematically, it can be represented as:
p = m * v
The kinetic energy (KE) of an object is defined as the energy possessed by an object due to its motion. Mathematically, it can be represented as:
KE = 1/2 * m * v^2
where m is the mass of the object and v is its velocity.
Given that the two particles have equal momentum, we can write:
m1 * v1 = m2 * v2
where m1 and m2 are the masses of the particles, and v1 and v2 are their velocities.
We are also given the masses of the particles: m1 = 2g and m2 = 4g. Let's assume their velocities to be v1 and v2 respectively.
Since the momentum is equal, we can write:
2g * v1 = 4g * v2
Dividing both sides by 2g, we get:
v1 = 2v2
Now, we can substitute this value of v1 in the equation for kinetic energy:
KE1 = 1/2 * 2g * (2v2)^2
= 1/2 * 2g * 4v2^2
= 4g * v2^2
Similarly, for the second particle:
KE2 = 1/2 * 4g * v2^2
= 2g * v2^2
To find the ratio of their kinetic energies (KE1 : KE2), we divide KE1 by KE2:
KE1/KE2 = (4g * v2^2) / (2g * v2^2)
= 4/2
= 2/1
Therefore, the ratio of their kinetic energies is 2:1. Hence, option A is the correct answer.
Explanation:
To solve this problem, we need to understand the relationship between momentum and kinetic energy.
The momentum (p) of an object is defined as the product of its mass (m) and velocity (v). Mathematically, it can be represented as:
p = m * v
The kinetic energy (KE) of an object is defined as the energy possessed by an object due to its motion. Mathematically, it can be represented as:
KE = 1/2 * m * v^2
where m is the mass of the object and v is its velocity.
Given that the two particles have equal momentum, we can write:
m1 * v1 = m2 * v2
where m1 and m2 are the masses of the particles, and v1 and v2 are their velocities.
We are also given the masses of the particles: m1 = 2g and m2 = 4g. Let's assume their velocities to be v1 and v2 respectively.
Since the momentum is equal, we can write:
2g * v1 = 4g * v2
Dividing both sides by 2g, we get:
v1 = 2v2
Now, we can substitute this value of v1 in the equation for kinetic energy:
KE1 = 1/2 * 2g * (2v2)^2
= 1/2 * 2g * 4v2^2
= 4g * v2^2
Similarly, for the second particle:
KE2 = 1/2 * 4g * v2^2
= 2g * v2^2
To find the ratio of their kinetic energies (KE1 : KE2), we divide KE1 by KE2:
KE1/KE2 = (4g * v2^2) / (2g * v2^2)
= 4/2
= 2/1
Therefore, the ratio of their kinetic energies is 2:1. Hence, option A is the correct answer.
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