Courses
Courses for Kids
Free study material
Offline Centres
More
Store

# Why is gravitational mass equal to inertial mass?

Last updated date: 17th Sep 2024
Total views: 352.2k
Views today: 4.52k
Verified
352.2k+ views
Hint: The value of inertial mass and gravitational mass of a particle are the same as the result of the "equivalence principle".
It is an essential principle for any metric theory of gravity like general relativity.
Gravitational mass and inertial mass are not equal.

Complete step-by-step solution:
Gravitational acceleration on the Earth is $9.8m/{s^2}$. Inertial acceleration can have various values. Inertial mass is distributed over the volume of the body. but the gravitational mass is always located at the center of the body.
Inertial mass is the parameter that gives the inertial resistance to an acceleration of the body when responding to all types of force.
Gravitational mass is described by the gravitational force strength experienced by the body when in the gravitational field
the force equation: $f = {m_i}a$
where $f$ is the force, aa is the acceleration, and
${m_i}$is the inertial mass. measuring the inertial mass of some object by applying a known force, measuring the trajectory to determine the acceleration, and dividing to find the inertial mass.
the force law for electrostatics $f = qE$
where $E$ is the electric field and
$q$ is the electric charge of the particle.
The particles can have different electric charges - some positive, some negative, and some zero.
now combine the equation we get charge to mass ratio as follows
$a = \dfrac{q}{{{m_i}}}E\quad$
And,
$a = \dfrac{{{m_{grav}}}}{{{m_i}}}g$
In gravity, the ratio of "gravitational charge" to inertial mass is the same as far as we know for all objects.

Note:When the field is an electric field, the particles will accelerate at a different amount. They will accelerate identically For the gravitational field From the Gravitation law, the force of gravitation between two bodies is proportional to their inertial masses.