Answer:
m2 = 83.3 g
Explanation:
by conservation of momentum principle we have
[tex]m_1v_{i1} + m_2v_{i2} = m_2v_{f2}[/tex]
as both sphere has same speed so [tex]v_{i2} = v_{i1}[/tex]
[tex]m_2 = \frac{m_1}[\frac{v_f2}{v_{f1}}+1}[/tex]
from conservation of kinetic energy principle we have
[tex]\frac{1}{2}m_1v^{2}_{i1} + \frac{1}{2}m_2v^{2}_{i2} = \frac{1}{2}m_2v^{2}_f2[/tex]
[tex]v_{f1} = \sqrt {\frac{(m_1+m_2) v^2_i1}{m_2}[/tex]
[tex] v_{f1} = v_{i2}\sqrt {\frac{(m_1+m_2)}{m_2}[/tex]
[tex]\frac{v_{f1}}{v_{i2}} =\sqrt {\frac{(m_1+m_2)}{m_2}[/tex]
substituting this value in above equation to get m2 value
[tex]m_2 = \frac{m_1}{\sqrt {\frac{(m_1+m_2)}{m_2}+1}}[/tex]
solving for m2 we get
[tex]m2 = \frac{m_1}{3}[/tex]
m_1 = 250 g
[tex]=\frac{250}{3}[/tex]
m2 = 83.3 g
