Match the Column I with Column II. 1|c| Column I 2c| Column II (A) For translatio

step 1 In this question we have to match the column first with column second. So for column first we ha

Match the Column I with Column II. 1|c| Column I 2c| ...

Match the Column I with Column II. \begin{tabular}{|l|l|l|l|} \hline \multicolumn{1}{|c|} { Column I } & \multicolumn{2}{c|} { Column II } \\ \hline (A) & For translational equilibrium & (p) & $M k^{2}$ \\ \hline (B) & For rotational equilibrium & (q) & Angular acceleration \\ \hline (C) & Moment of inertia of a body & (r) & $\sum \vec{F}=0$ \\ \hline (D) & Torque is required to produce & (s) & $\sum \vec{\tau}=0$ \\ \hline \end{tabular} (a) $\mathrm{A}-\mathrm{p}, \mathrm{B}-\mathrm{q}, \mathrm{C}-\mathrm{r}, \mathrm{D}-\mathrm{s}$ (b) $\mathrm{A}-\mathrm{q}, \mathrm{B}-\mathrm{r}, \mathrm{C}-\mathrm{s}, \mathrm{D}-\mathrm{p}$ (c) $\mathrm{A}-\mathrm{r}, \mathrm{B}-\mathrm{q}, \mathrm{C}-\mathrm{p}, \mathrm{D}-\mathrm{s}$ (d) $\mathrm{A}-\mathrm{r}, \mathrm{B}-\mathrm{s}, \mathrm{C}-\mathrm{p}, \mathrm{D}-\mathrm{q}$

Match the Column I with Column II. \begin{tabular}{|l|l|l|l|}
\hline \multicolumn{1}{|c|} { Column I } & \multicolumn{2}{c|} { Column II } \\
\hline (A) & For translational equilibrium & (p) & $M k^{2}$ \\
\hline (B) & For rotational equilibrium & (q) & Angular acceleration \\
\hline (C) & Moment of inertia of a body & (r) & $\sum \vec{F}=0$ \\
\hline (D) & Torque is required to produce & (s) & $\sum \vec{\tau}=0$ \\
\hline
\end{tabular}
(a) $\mathrm{A}-\mathrm{p}, \mathrm{B}-\mathrm{q}, \mathrm{C}-\mathrm{r}, \mathrm{D}-\mathrm{s}$
(b) $\mathrm{A}-\mathrm{q}, \mathrm{B}-\mathrm{r}, \mathrm{C}-\mathrm{s}, \mathrm{D}-\mathrm{p}$
(c) $\mathrm{A}-\mathrm{r}, \mathrm{B}-\mathrm{q}, \mathrm{C}-\mathrm{p}, \mathrm{D}-\mathrm{s}$
(d) $\mathrm{A}-\mathrm{r}, \mathrm{B}-\mathrm{s}, \mathrm{C}-\mathrm{p}, \mathrm{D}-\mathrm{q}$

Key Concepts

Translational Equilibrium

Translational equilibrium occurs when the net force acting on a body is zero, meaning all the individual forces balance each other so that the body does not accelerate along any straight-line path. This concept is fundamental in mechanics and enables us to analyze the stability of structures and systems in which forces are applied in various directions.

Rotational Equilibrium

Rotational equilibrium is achieved when the net torque acting on a body is zero; that is, the sum of all torques (moments) about any axis cancels out. This condition ensures that there is no angular acceleration, and thus the body does not start rotating or changes its rotational state.

Moment of Inertia

The moment of inertia is a measure of an object's resistance to changes in its rotational motion about a particular axis. It depends on the mass distribution of the object relative to that axis and plays a role analogous to mass in linear motion, affecting how the object responds to applied torques.

Torque

Torque is a measure of the tendency of a force to cause an object to rotate about an axis. It depends on both the magnitude of the force and the perpendicular distance from the axis of rotation to the line of action of the force. Torque is a central concept in analyzing rotational motion and mechanical systems.

Angular Acceleration

Angular acceleration is the rate at which an object's rotational speed changes with time. It results from a net torque acting on the object in conjunction with its moment of inertia, as described by Newton's second law for rotational motion. This concept is vital for understanding how rotational dynamics are initiated and modified.

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