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A 4 kg mass and 1 kg are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is [1989]
  • a)
    1 : 2
  • b)
    1 : 1
  • c)
    2 : 1
  • d)
    4 : 1
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A 4 kg mass and 1 kg are moving with equal kinetic energies. The ratio...
. Hence, mv = (2mE)1/2. For same
KE, momentum   Hence, the ratio is 2 : 1.
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A 4 kg mass and 1 kg are moving with equal kinetic energies. The ratio...
Solution:
Given, mass of object 1 (m1) = 4 kg
mass of object 2 (m2) = 1 kg
Both objects have equal kinetic energy.
Let the velocities of objects 1 and 2 be v1 and v2 respectively.
Kinetic energy of an object is given by:
K = (1/2)mv^2
Given that the kinetic energy of both objects is equal i.e., K1 = K2
Therefore, (1/2)m1v1^2 = (1/2)m2v2^2
Simplifying the above equation, we get:
v2/v1 = √(m1/m2)
We know that the momentum of an object is given by:
p = mv
Therefore, the ratio of the magnitudes of their linear momenta is given by:
p1/p2 = m1v1/m2v2
Substituting v2/v1 = √(m1/m2), we get:
p1/p2 = m1/m2 * v1/v2
p1/p2 = m1/m2 * v1/(√(m1/m2)v1)
p1/p2 = √(m1/m2)
Substituting the values of m1 and m2, we get:
p1/p2 = √(4/1)
p1/p2 = 2
Therefore, the ratio of the magnitudes of their linear momenta is 2:1. Hence, the correct option is (c).
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