Two bodies of masses 4g and 16g are moving with equal Kientic energy then the ratio of their momentum will be answer is 1:2 but how?

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Answer 1 · 2018-07-12T20:15:05

Explanation is below

Let #v_1# & #v_2# be the velocities of mass #m_1=4\ g# & #m_2=16\ g# respectively then their kinetic energies are equal as follows

#\frac{1}{2}m_1v_1^2=1/2 m_2v_2^2#

#\frac{1}{2}(4)v_1^2=1/2 (16)v_2^2#

#v_1^2=4v_2^2#

#v_1=2v_2#

Now, the ratio of their momenta #m_1v_1# & #m_2v_2# is given as

#\frac{m_1v_1}{m_2v_2}=\frac{(4)(2v_2)}{(16)v_2}=1/2#

Proved