Question

The ratio of gravitational mass to inertial mass is equal to
A. $\dfrac{1}{2}$
B. 2
C. 1
D. None of these

Answer 1

Hint: The mass found just by applying a force and calculating its acceleration is called inertial mass. The mass found by knowing the weight of the body and dividing its weight by g is called gravitational mass.

Complete step by step answer:

The tendency or ability of a body to resist any change in its state of rest or uniform motion is called the inertia of the body. Inertia of a body depends on mass. It is also called the inertial mass of a body.
We all know that when an unbalanced force is applied on a body, the body accelerates. However, when we apply the same force on a couple number of bodies, all the bodies do not move with the same acceleration. This is because of the inertial mass of the bodies.
Mass is defined as the amount of matter inside a body. Different bodies have different masses. Therefore, different bodies move with different acceleration when the same force is applied on all the bodies.
The relation between force applied F, mass of the given body m and its acceleration a is given by Newton’s second law, F=ma.
$\Rightarrow m=\dfrac{F}{a}$.
We find the mass of the body by dividing the force applied on it with its acceleration. This mass is called inertial mass.
There is one more way to find the mass of a body. That is with the help of gravity. Due to earth’s gravity , any body near earth’s surface experiences a gravitational force equal to mg, where g is the acceleration of the given body due the gravitational force. g is constant near the surface of earth and is equal to $9.8m{{s}^{-2}}$. With this information, we can find the mass of the body.
Suppose an unknown body is near the surface of earth. The force exerted on it will be F=mg. Therefore, if we know the force F i.e. the weight of the body, we can find the mass and it will be equal to $m=\dfrac{F}{g}$. The mass found in this way is called gravitational mass.
We can now understand that there is nothing like inertial mass and gravitational mass in reality. However, we name the same mass depending on the way it is found.
The mass found just by applying a force and calculating its acceleration is called inertial mass.
The mass found by knowing the weight of the body and dividing its weight by g is called gravitational mass.
Therefore, if mass of a body is found by both the methods then its inertial mass and gravitational are the same. Hence, the ratio of gravitational mass and inertial mass will be 1.
Therefore, the correct option is C.

Note: If there is confusion between inertial mass and gravitational mass, think in this way that there is nothing like inertial mass and gravitational mass. There is only one type and it is called the ‘mass’ of the body and mass is the amount of matter contained in a body.
It correlates with the fact that we all humans are the same (belong to the same species) but still we separate ourselves on the basis of origin.