Odpowiedź:
[tex]\huge\boxed{E. \ 4m_1 = m_2}[/tex]
Wyjaśnienie:
Moment bezwładności kuli określany jest wzorem
[tex]I = \frac{2}{5}mR^{2}\\\\R_2 = R\\R_1 = 2R\\\\to\\\\I_1 = \frac{2}{5}m_1R^{2}_1 =\frac{2}{5}m_1\cdot(2R)^{2} = \frac{2}{5}m_1\cdot4R^{2}=\frac{8}{5}m_1R^{2}\\\\I_2 = \frac{2}{5}m_2R_2^{2} = \frac{2}{5}m_2R^{2}\\\\I_1 = I_2\\\\\frac{8}{5}m_1R^{2} = \frac{2}{5}m_2R^{2} \ \ \ /:R^{2}\\\\8m_1 = 2m_2 \ \ \ /:2\\\\\boxed{4m_1 = m_2}[/tex]
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Odpowiedź:
[tex]\huge\boxed{E. \ 4m_1 = m_2}[/tex]
Wyjaśnienie:
Moment bezwładności kuli określany jest wzorem
[tex]I = \frac{2}{5}mR^{2}\\\\R_2 = R\\R_1 = 2R\\\\to\\\\I_1 = \frac{2}{5}m_1R^{2}_1 =\frac{2}{5}m_1\cdot(2R)^{2} = \frac{2}{5}m_1\cdot4R^{2}=\frac{8}{5}m_1R^{2}\\\\I_2 = \frac{2}{5}m_2R_2^{2} = \frac{2}{5}m_2R^{2}\\\\I_1 = I_2\\\\\frac{8}{5}m_1R^{2} = \frac{2}{5}m_2R^{2} \ \ \ /:R^{2}\\\\8m_1 = 2m_2 \ \ \ /:2\\\\\boxed{4m_1 = m_2}[/tex]