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Two particles of masses 2g and 4g have equal momentum. What is the ratio between their kinetic energies?
- a)1:3
- b)3:1
- c)1:2
- d)2:1
Correct answer is option 'D'. 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:
1. The formula for momentum is given by p = mv, where p is the momentum, m is the mass, and v is the velocity.
2. Let the velocity of the two particles be v1 and v2 respectively.
3. Given that the masses of the two particles are 2g and 4g respectively and their momenta are equal, we can write the equation as:
(2g)(v1) = (4g)(v2)
4. Solving for v2 in terms of v1, we get:
v2 = (1/2)v1
5. The kinetic energy of a particle is given by the formula KE = (1/2)mv^2, where KE is the kinetic energy, m is the mass, and v is the velocity.
6. The ratio of the kinetic energies of the two particles can be found by substituting the values of their masses and velocities into the formula for kinetic energy:
KE1/KE2 = (1/2)(2g)(v1)^2 / (1/2)(4g)(v2)^2
7. Simplifying the equation further, we get:
KE1/KE2 = (1/2)(2g)(v1)^2 / (1/2)(4g)((1/2)v1)^2
KE1/KE2 = (1/2)(2g)(v1)^2 / (1/2)(4g)(1/4)(v1)^2
KE1/KE2 = 1/2
8. Therefore, the ratio of the kinetic energies of the two particles is 1:2, which corresponds to option D.
Explanation:
1. The formula for momentum is given by p = mv, where p is the momentum, m is the mass, and v is the velocity.
2. Let the velocity of the two particles be v1 and v2 respectively.
3. Given that the masses of the two particles are 2g and 4g respectively and their momenta are equal, we can write the equation as:
(2g)(v1) = (4g)(v2)
4. Solving for v2 in terms of v1, we get:
v2 = (1/2)v1
5. The kinetic energy of a particle is given by the formula KE = (1/2)mv^2, where KE is the kinetic energy, m is the mass, and v is the velocity.
6. The ratio of the kinetic energies of the two particles can be found by substituting the values of their masses and velocities into the formula for kinetic energy:
KE1/KE2 = (1/2)(2g)(v1)^2 / (1/2)(4g)(v2)^2
7. Simplifying the equation further, we get:
KE1/KE2 = (1/2)(2g)(v1)^2 / (1/2)(4g)((1/2)v1)^2
KE1/KE2 = (1/2)(2g)(v1)^2 / (1/2)(4g)(1/4)(v1)^2
KE1/KE2 = 1/2
8. Therefore, the ratio of the kinetic energies of the two particles is 1:2, which corresponds to option D.
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Two particles of masses 2g and 4g have equal momentum. What is the ratio between their kinetic energies?a)1:3b)3:1c)1:2d)2:1Correct answer is option 'D'. Can you explain this answer?
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