Question

The ratio of inertial mass to gravitational mass is equal to:
A.$0.5$
B.$1$
C.$1.5$
D.$2$

Answer 1

Hint: Inertial mass is the mass of an inertial frame of reference. It is expressed as the ratio of the force acting on the body divided by its acceleration. The gravitational mass is the mass that is involved in the gravitational force of attraction between two bodies.

Complete step-by-step answer:
The inertial mass of a body can be defined as resistance to acceleration. When a force acts on a body, it is usually accelerated. The property of a body to resist the acceleration produced by force is called the inertial mass. It is evident from Newton's second law of motion which can be expressed mathematically as, $F=ma$, where m is the inertial mass of the body, a is the acceleration of the body. So, the inertial mass can be expressed as,
$m=\dfrac{F}{a}$
When two bodies of mass M and m are separated by a distance of r, the gravitational force of attraction of the two bodies is given by,
$F=\dfrac{GMm}{{{r}^{2}}}$
The mass m associated with this force is known as the gravitational mass.
Usually, the gravitation mass and the inertial mass are the same, so the ratio between them is 1.
So, the answer to the question is option (C).

Note:
- If the same force is applied to two bodies of unequal mass, the maximum acceleration will be produced by the body which has a smaller mass compared to the other.
- If g is the acceleration due to gravity at a place, then the force acting on a mass m can be written as, $F=mg$, where m is the gravitational mass.
- The acceleration due to gravity is not constant. It varies with altitude and depth from the surface of the planet.