System Of Particles And Rotational Motion Ques 50

Answer:

Correct Answer: 50.(a)

Solution:

50. (a) Let body contain $m_1, m_2, m_3 \ldots \ldots . m_n$ masses at distance $r_1, r_2, r_3 \ldots \ldots . . r_n$ from axis $O A$.

Angular momentum of body

$=m_1 v_1 r_1+m_2 v_2 r_2 \ldots . .+m_n v_n r_n$

$=m_1(\omega r_1) r_1+m_2(\omega r_2) r_2 \ldots \ldots+m_n(\omega r_n) r_n$

$=(m_1 r_1^{2}) \omega+(m_2 r_2^{2}) \omega \ldots \ldots .+(m_n r_n^{2}) \omega$

$=(\sum _{i=1}^{n} m_i r_i^{2}) \omega=I \omega$