Physics MCQs for NEET — Practice Questions with Answers

The moment of inertia about AD = ? $ I = m_1 (Perpendicular distance of m_1 from AD)^2 + m_2 (Perpendicular distance of m_2 from AD)^2 + m_3 (Perpendicular distance of m_3 from AD)^2 $ $ = 0 + m_2 \times \left( { 9 \over 2} \right) ^2 + m_3 \times \left( { 9 \over 2} \right) ^2 $ $ = ( m_2 + m_3 ) { a^2 \over 4 } $

$ I_A = m_a r_a^2 , I_B = m_b r_b^2 $ $ \therefore { I_B \over I_A} = { m_b \over m_a } \times \left( { r_b \over r_a } \right) ^2 $ Let K is the mass of unit length of the wire then $ m_a = ( 2 \pi r_a ) k and m_b = ( 2 \pi r_b ) K $ $ \therefore { m_b \over m_a } = { r_b \over r_a} $ $ \therefore { I_B \over I_A } = 8 = \left( { m_b \over m_a } \right) \left( { r_b \over r_a } \right) ^2 = \left( {r_b \over r_a } \right) ^3 $ $ \therefore { r_b \over r_a } = 2 $

Let M be the mass and $R_1$ the initial radius of the earth $ \omega_1 $ is the angular veloalty of the rotation of the earth, the duration $T_1$ of the day $ T_1 = { 2 \pi \over \omega_1 } $ and $ T_2 = { 2 \pi \over \omega_2 } $ According to law of conservation of angular momentum $ I_1 \omega_1 = I_2 \omega_2 $

$ m_1 = 1 , m_2 = 35.5 ,r_1 = 0 , r_2 = 1.27 \hat i $ $ \vec r_{cm} = { m_1 \vec r_1 + m_2 \vec r_2 \over m_1 + m_2} $

Theory [B] The centre of mass of lucky remains uncharged.

$ \omega_0 { G_0 \over r} = { 72 \times 1000 /3600 \over 0.25 } = 80 rad /sec $ $ \omega = 0 . \theta = 2 \pi n = 2 \pi \times 20 = 40 \pi rad $ $ As \;2 \alpha \theta = w^2 - w_0^2 $

$ \theta = wot + { 1 \over 2} \alpha t^2 \Rightarrow \theta = 100 rad $

$ I = { 1 \over 2 } MR^2 = { 1 \over 2} ( \pi R^2 t \times \rho ) R^2 $ $ A t \times \rho are same $ $ I \alpha R^4 \therefore { I_1 \over I_2 } = \left( { R_1 \over R_2 } \right) ^4 $

$ I = MK^2 = 160 $ $ \therefore K^2 = {160 \over m} = { 160 \over 10 } = 16 $ $ \therefore K = 4 $

$ { I ring \over I disc } = { MR^2 \over { 1 \over 2 } MR^2 } = { 2 \over 1 } $ $ \therefore 2 :1 $