If a light object (mass M_1 and velocity V_1) | vedclass

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(D) The kinetic energy $(KE)$ of an object is given by $KE = \frac{P^2}{2M}$,where $P$ is the momentum and $M$ is the mass.Given that both objects hav

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$M_2 V_2 > M_1 V_1$

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(D) The kinetic energy $(KE)$ of an object is given by $KE = \frac{P^2}{2M}$,where $P$ is the momentum and $M$ is the mass.Given that both objects have the same kinetic energy,we have $KE_1 = KE_2$.This implies $\frac{P_1^2}{2M_1} = \frac{P_2^2}{2M_2}$.Rearranging the terms,we get $\frac{P_1^2}{P_2^2} = \frac{M_1}{M_2}$,which simplifies to $\frac{P_1}{P_2} = \sqrt{\frac{M_1}{M_2}}$.Since the second object is heavier,we have $M_2 > M_1$.Therefore,$\sqrt{\frac{M_2}{M_1}} > 1$,which means $P_2 > P_1$.Thus,the momentum of the heavy object is greater than the momentum of the light object,i.e.,$M_2 V_2 > M_1 V_1$.

If a light object (mass $M_1$ and velocity $V_1$) and a heavy object (mass $M_2$ and velocity $V_2$) have the same kinetic energy,then which of the following is true regarding their momenta ($P_1 = M_1 V_1$ and $P_2 = M_2 V_2$)?

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