Question

Which of the following has the same dimension as that of torque?
(A) Moment of force.
(B) pressure.
(C) acceleration.
(D) impulse.

Answer 1

In order to find the dimension of torque, we have to know the relation to which the torque is connected. The torque is connected to distance, force and the angle between force and the distance. Similarly have to analyse the given options for similar properties.

Complete answer:
Torque: The term torque can be explained as the rotation proportional to that of the linear force. Torque is calculated as a force that can make an object rotate on an axis. Torque is the force that makes an object to obtain angular acceleration. Since torque has direction as well as magnitude it is a vector quantity. The torque can be expressed as,
$T = F \times r \times \sin \theta$
Where,
$T$ denotes the torque,
$F$ denotes the linear force,
$r$ denotes the distance between the axis of rotation and the application of linear force takes place,
$\sin \theta$ denotes the angle between $F$ and $r$ .
The respective S.I. unit for the torque equation;
$\Rightarrow T = kgm{s^{ - 2}} \times m$
Since $\sin \theta$ does not have any S.I. unit;
$\Rightarrow T = kg{m^2}{s^{ - 2}}$
Therefore, the dimension of torque is;
$\Rightarrow Torque = M{L^2}{T^{ - 2}}$
Where,
$M$ denotes the mass,
$L$ denotes the length,
$T$ denotes the time.
Moment of force:
Similarly, the moment of force is a calculation of its own disposition to make the body rotate on a specific axis. The magnitude of the moment acting on a particular point or axis is sprightly proportional to the distance of the force from the axis. It is explained as the result of the force $F$ and the distance $r$.
The formula for moment of force if,
$\Rightarrow M = r \times F$
where,
$M$ denotes the moment of force,
$r$ denotes the distance between the applied force to the object,
$F$ denotes the applied force.
The respective S.I. units are;
$\Rightarrow T = m \times kg m{s^{ - 2}}$
$\Rightarrow T = kg{m^2}{s^{ - 2}}$
Therefore, the dimensions of moment of force are;
$\Rightarrow Moment\,of\,force = M{L^2}{T^{ - 2}}$
Where,
$M$ denotes the mass,
$L$ denotes the length,
$T$ denotes the time.
Therefore, both torque and moment of force have the same dimensions.

Hence, option (A), moment of force is the correct answer.

Note: The expression of the unit of the physical quantity in the form of fundamental quantities is known as the Dimensional quantity. Some of the fundamental quantities are mass $\left( M \right)$ , length $\left( L \right)$ , time $\left( T \right)$. The fundamental formulas are the same throughout the world.