Question

What is not the unit of Force?
(a). Pound
(b). Dyne
(c). Joule
(d). Newton

Answer 1

- Hint: Force deals with movement, speed, mass and direction and has been derived based on these terms. Perform the dimensional analysis on the quantity force. And compare the units of the options to the units of the quantity questioned.

Complete step-by-step solution -

To answer this question, we shall have to understand what is the definition of force and a brief history about it. So, force usually means the applied effort to move some object from its original point and is mostly explained in terms of Isaac Newton’s law of motion. According to Newton's law, a body is at rest or remains stationary until a force is applied. Sir Isaac Newton was the first scientist to study about force. Though, there are different types of force, it is just as a push or a pull on a body.
Force is expressed as the product of mass and acceleration and since it deals with direction, it is a vector quantity. The formula of force is given as,
\[F=ma\],
Where F is force applied, m is mass and a is acceleration applied on the mass to make the movement.
To know the unit of force, we shall express acceleration in terms of velocity and time.
\[a=\dfrac{v}{t}\],
Here, v is velocity and t is time. Velocity is measured in meter/second (m/s) and time in seconds(s). Hence, the unit for acceleration is,
\[a=\dfrac{v}{t}=\dfrac{\dfrac{m}{s}}{s}=\dfrac{m}{{{s}^{2}}}\],
Hence the unit of force will be,
\[F=ma=kg\dfrac{m}{{{s}^{2}}}\],
Here, kg is kilogram. This is equal to one Newton and hence in S.I (International Standard Units) the unit of force is Newton.
Also, force can be expressed in terms of momentum. If p is momentum, t is time, then the force can be expressed as the rate of change of momentum and hence can be expressed as,
\[F=\dfrac{p}{t}=\dfrac{mv}{t}\],
Here momentum is a product of mass and velocity.
In other units, it can be expressed as Dyne which is as follows,
\[F=ma=\dfrac{mv}{t}=\dfrac{gcm}{{{s}^{2}}}\],
Here, g is grams and cm is centimetres. Also, sometimes. Foot-Pound-Second (FPS) systems are used to express force. Hence, its unit will be in pounds.
Now, we can say force can be expressed as Newton, Dyne and Pound. Hence, joule is not the unit of force.

Note: Joule is the correct answer because it is the unit of energy. Energy for an object is defined as the work done on the object. Mathematically, the energy is given by force times the displacement. Therefore, force cannot have the same unit as energy.