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#	Question	Answer
1	What is a rigid body?	A body with a perfectly definite and unchanging shape. The distances between all pairs of particles of such a body do not change.
2	Is the rolling of a cylinder down an inclined plane pure translational motion?	No. It is a combination of translational and rotational motion.
3	What is the position of the centre of mass of a two-particle system of masses \( m_1 \) and \( m_2 \) located at \( x_1 \) and \( x_2 \) respectively?	\( X = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2} \).
4	Where does the centre of mass of a homogeneous thin rod lie?	At its geometric centre.
5	Where does the centre of mass of a triangular lamina lie?	At the centroid of the triangle (the point of intersection of the medians).
6	What is the total linear momentum of a system of particles?	\( \mathbf{P} = M\mathbf{V} \), where \( M \) is the total mass and \(\mathbf{V}\) is the velocity of the centre of mass.
7	What is the magnitude of the vector product of two vectors \(\mathbf{a}\) and \(\mathbf{b}\)?	\( ab \sin\theta \), where \(\theta\) is the angle between the two vectors.
8	What is the value of \(\mathbf{a} \times \mathbf{a}\)?	Zero (null vector).
9	What is the relation between the linear velocity \(\mathbf{v}\) and the angular velocity \(\boldsymbol{\omega}\) of a particle in a rigid body rotating about a fixed axis?	\( \mathbf{v} = \boldsymbol{\omega} \times \mathbf{r} \).
10	What is the magnitude of the torque?	\( \tau = r F \sin\theta = r_\perp F = r F_\perp \).
11	What is the relation between the torque acting on a particle and its angular momentum?	\( \frac{d\mathbf{l}}{dt} = \boldsymbol{\tau} \).
12	What are the conditions for the mechanical equilibrium of a rigid body?	The net external force is zero and the net external torque is zero: \( \sum \mathbf{F}_i = 0 \) and \( \sum \boldsymbol{\tau}_i = 0 \).
13	What is a couple?	A pair of equal and opposite forces with different lines of action. A couple produces pure rotation without translation.
14	Under what condition does the centre of gravity coincide with the centre of mass?	When the gravitational field is uniform.
15	What is the moment of inertia of a system of particles about a given axis?	\( I = \sum m_i r_i^2 \), where \( r_i \) is the perpendicular distance of the \( i \)th particle from the axis.
16	Does the moment of inertia of a body depend on the choice of the axis?	Yes.
17	What is the moment of inertia of a thin circular ring of mass \( M \) and radius \( R \) about its diameter?	\( \frac{MR^2}{2} \).
18	What are the kinematic equations for rotational motion with uniform angular acceleration?	\( \omega = \omega_0 + \alpha t \), \( \theta = \theta_0 + \omega_0 t + \frac{1}{2}\alpha t^2 \), \( \omega^2 = \omega_0^2 + 2\alpha(\theta - \theta_0) \).
19	What is the relation between torque and angular acceleration for a rigid body rotating about a fixed axis?	\( \tau = I\alpha \).
20	What is the rotational analogue of Newton's second law \( F = ma \)?	\( \tau = I\alpha \).
21	What is the form of the conservation of angular momentum for rotation about a fixed axis?	\( I\omega = \text{constant} \) (when external torque is zero).
22	What is the dimensional formula of torque?	\( [ML^2T^{-2}] \).
23	Are the angular momentum \(\mathbf{L}\) and the angular velocity \(\boldsymbol{\omega}\) necessarily parallel?	No. However, for a rigid body rotating about a fixed axis of symmetry, \(\mathbf{L} = I\boldsymbol{\omega}\).
24	A solid cylinder of mass 20 kg and radius 0.25 m rotates about its axis with angular speed 100 rad s⁻¹. What is its rotational kinetic energy?	3125 J (from \( I = \frac{1}{2}MR^2 = 0.625\,\mathrm{kg\,m^2} \) and \( K = \frac{1}{2}I\omega^2 \)).
25	Find the centre of mass of a uniform L-shaped lamina made of three 1 m × 1 m squares (total mass 3 kg), with the squares' own centres at (1/2,1/2), (3/2,1/2) and (1/2,3/2).	(5/6 m, 5/6 m), treating each square's mass as concentrated at its own geometric centre.
26	For the same ladder, what is the magnitude and direction of the floor's reaction force?	≈199 N, at about 80° to the horizontal — combining the vertical normal reaction (196 N) and horizontal friction (≈34.6 N).
27	What does the scalar triple product \( \mathbf{a}\cdot(\mathbf{b}\times\mathbf{c}) \) represent geometrically?	Its magnitude equals the volume of the parallelepiped formed by the three vectors a, b, and c.
28	A 1800 kg car has its axles 1.8 m apart, with its centre of gravity 1.05 m behind the front axle (g = 9.8 m s⁻²). What force does the ground exert on each front wheel and each back wheel?	≈3675 N on each front wheel, ≈5145 N on each back wheel (the back axle carries 1050 kgf total, the front 750 kgf, from moments about each axle).
29	(NEET 2020) A 5 kg particle and a 10 kg particle sit at the ends of a 1 m massless rod. How far is the centre of mass from the 5 kg particle?	≈0.67 m ( \( 2/3\,\mathrm{m} \) ), from \( X = (5 \times 0 + 10 \times 1)/15 \).