Explanation
Newton's First Law of Motion states that a body at rest will remain at rest unless an outside force acts on it, and a body in motion at a constant velocity will remain in motion in a straight line unless acted upon by an outside force.
If a body experiences an acceleration ( or deceleration) or a change in direction of motion, it must have an outside force acting on it. Outside forces are sometimes called net forces or unbalanced forces. The property that a body has that resists motion if at rest, or resists speeding or slowing up, if in option, is called inertia. Inertia is proportional to a body's mass, or the amount of matter that a body has. The more mass a body has, the more inertia it has.
The Second Law of Motion states that if an unbalanced force acts on a body, that body will experience acceleration ( or deceleration), that is, a change of speed. One can say that a body at rest is considered to have zero speed, ( a constant speed). So any force that causes a body to move is an unbalanced force. Also, any force, such as friction, or gravity, that causes a body to slow down or speed up, is an unbalanced force. This law can be shown by the following formula $$ F= ma$$
$$\textbf{Hint}$$ Apply newton's second law of motion.
STEP (1): SI Unit
Force acting on the body may affect the shape of the body or it will accelerate or decelerate the body, or it will give motion to the static body or it will stop the motion of the dynamic body.
$$F = ma$$
Where $$'F'$$ = force applied, $$'m'$$ = mass and $$'a'$$ = acceleration
Acceleration $$a = \dfrac vt$$
Where $$v$$ = velocity (in m/s)
Here $$'m'$$ is mass and $$'s'$$ is seconds
Time $$'t'$$ is in seconds
Therefore acceleration unit is = $$\dfrac{\dfrac ms}s = \dfrac m{s^2}$$
Hence unit of force = $$kg \dfrac m{s^2} = Newton$$ (in S.I. unit) i.e, option $$D$$ is a unit of force
Newton can converted into Pound
that is 1 Newton = 0.22481 pound ( in FPS system ) i.e, option $$A $$ is unit of force
$$\textbf{Step2:CGS Unit}$$
$$F = \dfrac{g.cm}{s^2} = Dyne$$ (in C.G.S. unit) i.e, option $$ B $$ is a unit of force
Here $$'g'$$ is grams , $$'cm'$$ is centimeters and $$'s'$$ is seconds
Conclusion: Joule is the correct answer because it is the unit of energy.
The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
This verbal statement can be expressed in equation form as follows:
$$a=\dfrac{F}{m}$$
put $$a=g$$; gravitational acceleration,
So,
$$F=mg$$
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