Question

A cardinal (Richmondena cardinalis) of mass 4.20×10−2 kg and a baseball of mass 0.146 kg have the same kinetic energy. What is the ratio of the cardinal's magnitude pc of momentum to the magnitude pb of the baseball's momentum?

Answer 1

Explanation:

It is given that,

Mass of cardinal,$m_c=4.2\times 10^{-2}\ kg$

Mass of baseball, $m_b=0.146\ kg$

Both cardinal and baseball have same kinetic energy. We need to find the ratio of the cardinal's magnitude $p_c$ of momentum to the magnitude $p_c$ of the baseball's momentum.

$E_c=E_b$

Kinetic energy is given by, $E=\dfrac{p^2}{2m}$

$\dfrac{p_c^2}{2m_c}=\dfrac{p_b^2}{2m_b}$

$(\dfrac{p_c}{p_b})^2=\dfrac{m_c}{m_b}$

$\dfrac{p_c}{p_b}=\sqrt{\dfrac{m_c}{m_b}}$

$\dfrac{p_c}{p_b}=\sqrt{\dfrac{4.2\times 10^{-2}}{0.146}}$

So, $\dfrac{p_c}{p_b}=\dfrac{53}{100}$

So, the ratio of cardinal's magnitude of momentum to the magnitude of the baseball's momentum is 53 : 100