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Two particles of masses 1 g and 4 g have equal kinetic energies. What is the ratio between their momenta?
- a)1 : 4
- b)1 : 8
- c)1 : 2
- d)1 : 16
Correct answer is option 'C'. Can you explain this answer?
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Solution:
Given: Mass of particle 1 (m1) = 1 g = 0.001 kg
Mass of particle 2 (m2) = 4 g = 0.004 kg
Kinetic energy of both the particles is equal.
Let the kinetic energy be K.
K = 1/2*m1*v1^2 and K = 1/2*m2*v2^2
where v1 and v2 are the velocities of the two particles.
Dividing the two equations, we get:
v1^2/v2^2 = m2/m1
v1/v2 = √(m2/m1)
Now, we know that momentum (p) = mv
Therefore, the ratio of momentum of the two particles will be:
p1/p2 = m1v1/m2v2
p1/p2 = m1/m2 * v1/v2
Substituting the value of v1/v2, we get:
p1/p2 = m1/m2 * √(m2/m1)
p1/p2 = √(m1*m2/m2*m1)
p1/p2 = 1/√(m2/m1)
p1/p2 = √(m1/m2)
Substituting the values of m1 and m2, we get:
p1/p2 = √(1/4)
p1/p2 = 1/2
Therefore, the ratio of momentum of the two particles is 1:2.
Hence, the correct option is (c) 1:2.
Given: Mass of particle 1 (m1) = 1 g = 0.001 kg
Mass of particle 2 (m2) = 4 g = 0.004 kg
Kinetic energy of both the particles is equal.
Let the kinetic energy be K.
K = 1/2*m1*v1^2 and K = 1/2*m2*v2^2
where v1 and v2 are the velocities of the two particles.
Dividing the two equations, we get:
v1^2/v2^2 = m2/m1
v1/v2 = √(m2/m1)
Now, we know that momentum (p) = mv
Therefore, the ratio of momentum of the two particles will be:
p1/p2 = m1v1/m2v2
p1/p2 = m1/m2 * v1/v2
Substituting the value of v1/v2, we get:
p1/p2 = m1/m2 * √(m2/m1)
p1/p2 = √(m1*m2/m2*m1)
p1/p2 = 1/√(m2/m1)
p1/p2 = √(m1/m2)
Substituting the values of m1 and m2, we get:
p1/p2 = √(1/4)
p1/p2 = 1/2
Therefore, the ratio of momentum of the two particles is 1:2.
Hence, the correct option is (c) 1:2.
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Two particles of masses 1 g and 4 g have equal kinetic energies. What is the ratio between their momenta?a)1 : 4b)1 : 8c)1 : 2d)1 : 16Correct answer is option 'C'. Can you explain this answer?
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