Rotational Motion MCQs for NEET — Physics Questions with Answers

The NCERT text states: 'By using symmetry consideration, we can easily show that the centres of mass of these bodies [homogeneous bodies of regular shapes like rings, discs, spheres, rods etc.] lie at their geometric centres.' For a thin rod, its geometric center is its midpoint.

The NCERT summary clearly defines the position vector of the centre of mass of a system of n particles as $R = \frac{1}{M} \sum m_i r_i$, where $M$ is the total mass of the system.

The NCERT text states: 'If we choose, the centre of mass as the origin of our coordinate system, $R = 0$, i.e., $\int r dm = 0$.' This implies that the weighted average position of all mass elements relative to the center of mass is zero.

The NCERT text provides the coordinates of the center of mass for a continuous mass distribution as $X = \frac{1}{M} \int x dm$, $Y = \frac{1}{M} \int y dm$, $Z = \frac{1}{M} \int z dm$. Since $M = \int dm$, options (2) and (3) are equivalent and both correctly represent the coordinates.

The summary states: 'In pure translation, every particle of the body moves with the same velocity at any instant of time.' This is a defining characteristic of pure translation.

The NCERT summary mentions: 'Velocity of the centre of mass of a system of particles is given by $V = P/M$, where $P$ is the linear momentum of the system.'

For a two-particle system, the general formula $R = \frac{1}{M} \sum m_i r_i$ simplifies to $X_{CM} = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2}$ for coordinates along a single axis. This is consistent with the initial discussion on the center of mass in the NCERT text.

In pure translation, according to the NCERT text and Figure 6.6(a), 'at any instant the velocities of any particles like O [center of mass] and P of the body are the same in pure translation.' Thus, option 4 describes a characteristic of combined translational and rotational motion, not pure translation.

Angular vectors (velocity, acceleration) lie along the axis of rotation by definition.

$k_{solid}^2 = \tfrac{2}{5}R^2$, $k_{hollow}^2 = \tfrac{2}{3}R^2$; ratio $k_s:k_h = \sqrt{3}:\sqrt{5}$ (often shown as $3:5$ for squared values).