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A stationary particle explodes into two particles of masses m1 and m2 which move in opposite directions with velocities v1 and v2. The ratio of their kinetic energies E1/E2 is [2003]
- a)m1v2/m2v1
- b)m2/m1
- c)m1/m2
- d)1
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A stationary particle explodes into two particles of masses m1 and m2 ...
From conservation law of momentum, before collision and after collision linear momentum (p) will be same. That is, initial momentum = final momentum.
Most Upvoted Answer
A stationary particle explodes into two particles of masses m1 and m2 ...
Explanation:
When a stationary particle explodes into two particles, the total momentum before and after the explosion remains conserved. This is due to the law of conservation of momentum.
Law of Conservation of Momentum:
The law of conservation of momentum states that the total momentum of a system remains constant if no external forces act on it. Mathematically, it can be expressed as:
Total momentum before explosion = Total momentum after explosion
Derivation of the Ratio of Kinetic Energies:
Let the initial mass of the stationary particle be m.
After the explosion, the two particles have masses m1 and m2, and velocities v1 and v2 respectively.
The total momentum before the explosion is:
Initial momentum = m × 0 (as the particle is initially stationary) = 0
The total momentum after the explosion is:
Final momentum = m1v1 - m2v2
Using the conservation of momentum, we can equate the initial and final momenta:
0 = m1v1 - m2v2
Simplifying the equation, we get:
m1v1 = m2v2
Derivation of the Ratio of Kinetic Energies:
The kinetic energy of a particle is given by the formula:
Kinetic energy = (1/2) × mass × velocity^2
The ratio of kinetic energies can be calculated as follows:
E1/E2 = [(1/2) × m1 × v1^2] / [(1/2) × m2 × v2^2]
Cancelling the common factors, we get:
E1/E2 = (m1v1^2) / (m2v2^2)
From the conservation of momentum equation, we know that m1v1 = m2v2. Substituting this value, we get:
E1/E2 = (m1v1^2) / (m2v2^2) = (m2v2^2) / (m2v2^2)
Simplifying the expression, we get:
E1/E2 = 1
Therefore, the ratio of kinetic energies E1/E2 is 1. Hence, the correct answer is option 'D'.
When a stationary particle explodes into two particles, the total momentum before and after the explosion remains conserved. This is due to the law of conservation of momentum.
Law of Conservation of Momentum:
The law of conservation of momentum states that the total momentum of a system remains constant if no external forces act on it. Mathematically, it can be expressed as:
Total momentum before explosion = Total momentum after explosion
Derivation of the Ratio of Kinetic Energies:
Let the initial mass of the stationary particle be m.
After the explosion, the two particles have masses m1 and m2, and velocities v1 and v2 respectively.
The total momentum before the explosion is:
Initial momentum = m × 0 (as the particle is initially stationary) = 0
The total momentum after the explosion is:
Final momentum = m1v1 - m2v2
Using the conservation of momentum, we can equate the initial and final momenta:
0 = m1v1 - m2v2
Simplifying the equation, we get:
m1v1 = m2v2
Derivation of the Ratio of Kinetic Energies:
The kinetic energy of a particle is given by the formula:
Kinetic energy = (1/2) × mass × velocity^2
The ratio of kinetic energies can be calculated as follows:
E1/E2 = [(1/2) × m1 × v1^2] / [(1/2) × m2 × v2^2]
Cancelling the common factors, we get:
E1/E2 = (m1v1^2) / (m2v2^2)
From the conservation of momentum equation, we know that m1v1 = m2v2. Substituting this value, we get:
E1/E2 = (m1v1^2) / (m2v2^2) = (m2v2^2) / (m2v2^2)
Simplifying the expression, we get:
E1/E2 = 1
Therefore, the ratio of kinetic energies E1/E2 is 1. Hence, the correct answer is option 'D'.
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A stationary particle explodes into two particles of masses m1 and m2 which move in opposite directions with velocities v1 and v2. The ratio of their kinetic energies E1/E2 is [2003]a)m1v2/m2v1b)m2/m1c)m1/m2d)1Correct answer is option 'B'. Can you explain this answer?
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