Question

The rotational analogue of force in linear motion is
A. Weight
B. angular momentum
C. moment of inertia
D. Torque

Answer 1

Hint: When we apply force on an object it will tend to move. If one end of the object is fixed then the object will rotate. The larger the applied force the larger the turning effect. We can see that the turning effect is more when we apply more force, the effect is less when we apply force near to the fixed point called the axis of rotation.

Formula used:
$\overrightarrow{L}=\overrightarrow{r}\times \overrightarrow{p}$
$I=\sum\limits_{i=1}^{n}{{{m}_{i}}{{r}_{i}}^{2}}$
$\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}$
Where symbols carry their usual meaning.

Complete answer:
The weight of an object is the gravitational pull towards the centre of earth and is equal to the product of the mass of the object and its acceleration due to the influence of gravity. So the weight of any object of mass \[m\] is $Weight=mg$ where $g$ the acceleration due to gravity of the object is. The weight of an object is always directed towards the centre of earth. So it is not a rotational analogue of force in linear motion.

Angular momentum: In linear motion the linear momentum of a body gives a measure of its translator motion. Analogous to linear momentum the angular momentum gives the measure of turning motion of the body. The angular momentum of a body rotating about a fixed axis is defined as the moment of linear momentum of the particle about that axis and is measured by the product of linear momentum and the perpendicular distance from the line of action.

Angular momentum, $\overrightarrow{L}=\overrightarrow{r}\times \overrightarrow{p}$.
So angular momentum is the rotational analogous to linear momentum.

Moment of inertia: The moment of inertia of a rigid body about a fixed axis is defined as the sum of the product of the masses of the particles constituting the system and the square of their respective distances from the axis of rotation. i.e.
$I=\sum\limits_{i=1}^{n}{{{m}_{i}}{{r}_{i}}^{2}}$
It is the rotational analogous mass of linear motion.

Torque: Torque is the turning effect of the force about the axis of rotation and is measured as the product of the magnitude of force and the perpendicular distance between the line of action of the force and the axis of rotation. Is given by
$\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}$

So, the correct answer is “Option D”.

Note:
Note that the torque is a vector quantity. Its direction is perpendicular to both the plane containing the force and the position vector of point of action. Also the torque is taken to be positive if the turning tendency is anti-clockwise and taken negative if it's clockwise.