Question

(a) Explain Newton’s first law of motion with an example.
(b) $F = \dfrac{{G{m_1}{m_2}}}{{{d^2}}}$ is the mathematical form of Newton’s law of gravitation. Give the statement of Newton’s law of gravitation.

Answer 1

Recall the statement for Newton’s first law of motion. Give the example of Newton’s first law of motion. Explain the different terms used in the equation for Newton’s law of gravitation and given the statement for Newton’s law of gravitation using this mathematical equation.

Complete step by step answer:
(a) The physicist Sir Isaac Newton gave three laws of motion of an object. Out of these three laws, the statement for Newton’s first law of motion is as follows:
“Until an external unbalanced force is applied on the object that object continues to be in its state of rest or of uniform motion.”
This tendency of the object to continue its state (of rest or of uniform motion) is known as inertia of the object.Therefore, Newton’s first law of motion is also known as law of inertia.
There are various examples of Newton’s first law of motion in everyday life.
For example, suppose a person is travelling in a vehicle in a straight line and the vehicle is moving with a uniform velocity. As the vehicle has uniform velocity, the person in the vehicle also has the same uniform velocity of motion in the forward direction. When the driver of the vehicle suddenly applies breaks, the vehicle stops suddenly. But the person in the vehicle moving with the uniform velocity of the vehicle tries to move in the same forward direction with the same uniform velocity even after the brakes are applied. The person’s motion with the vehicle stops after a sudden jerk in the forward direction. This shows that the person tries to move with his uniform velocity even after applying the break. Here, the break applied is the external unbalanced force.
(b) Newton’s gravitational law is given by the mathematical equation
$F = \dfrac{{G{m_1}{m_2}}}{{{d^2}}}$
Here, $F$ is the force of attraction between two objects, $G$ is universal gravitational constant, ${m_1}$ is the mass of first object, ${m_2}$ is the mass of second object and $d$ is the distance between the centres of two objects.
From this equation, we can state Newton’s law of gravitation as “any two objects in the universe have a force of attraction between them which is directly proportional to the product of mass of the two objects and inversely proportional to the square of the distance between centres of the two objects.”

Note: The students may think that in the statement for Newton’s law of gravitation, the term universal gravitational constant $G$ is not explained. It is the universal constant. Hence, it is used as a constant of proportionality in the relation given by Newton’s law of gravitation.