An object of mass 4 kg and another object of mass 1 kg are moving such that they have equal kinetic energies. The ratio of the magnitudes of their linear momenta is

Question

An object of mass 4 kg and another object of mass 1 kg are moving such that they have equal kinetic energies. The ratio of the magnitudes of their linear momenta is, 1 : 2, 1 : 1, 2 : 1, 4 : 1

MARKS App · Accepted Answer

K . E 1 of 4 kg mass = 1 2 ( 4 ) v 1 2 K . E 2 of 1 kg mass = 1 2 ( 1 ) v 2 2 Since, K . E 1 = K . E 2 (given) We have, 1 2 ( 4 ) v 1 2 = 1 2 ( 1 ) v 2 2 ⇒ v 1 v 2 = 1 4 = 1 2 Now, momentum | P ¯ | of 4 kg mass = ( 4 ) ( 1 ) k g m s and, momentum | P ¯ 2 | of 1 kg = ( 1 ) ( 2 ) k g m s ∴ | P ¯ 1 | | P ¯ 2 | = 4 2 = 2 1

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