Question

Two bodies m and 4m are moving with equal kinetic energy. The ratio of their linear momenta is_?​

Answer 1

so easy

see the attached file

please mark as brain list I have solved it twice

Answer 2

Given,

Mass of two bodies is m and 4m.

Let mass of one body be '$\mathsf{m_1}$ = m

Velcoity of 1st body = $\mathsf{v_1}$

Mass of another body, $\mathsf{m_2}$ = 4m

Velocity of 2nd body = $\mathsf{v_2}$

Now, Kinetic energy of 1st body = $\mathsf{\dfrac{1}{2}}{m_1} {v_1}^{2}$

Kinetic energy of 2nd body = $\mathsf{\dfrac{1}{2}}m_2{v_2}^{2}$

It is given that the K. E. ( Kinetic energy ) of both bodies are equal.

So,

$\mathsf{\dfrac{1}{2}}m_1{v_1}^{2}$ = $\mathsf{\dfrac{1}{2}}m_2{v_2}^{2}$

$\mathsf{m{v_1}^{2} \:=\:4m{v_2}^{2}}$

$\mathsf{\dfrac {{v_1} ^{2}}{{v_2}^{2}}\:=\:\dfrac{4m}{m}}$

$\mathsf{\dfrac{v_1}{v_2}}\:=\:\dfrac{2m}{m}$ ---> ( i )

Ratio of their linear momenta = $\mathsf{\dfrac{P_1}{P_2}}$

Ratio of their linear momenta = $\mathsf{\dfrac{m_1{v_1}}{m_2{v_2}}}$

Ratio of their linear momenta = $\mathsf{\dfrac{m* 2m}{4m*m}}$

Ratio of their linear momenta = $\mathsf{\dfrac {1}{2}}$

$\boxed{\boxed{\mathsf{RATIO\:=\:1\::\:2}}}$