The ratio of inertial mass and gravitational | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The gravitational force acting on a body is given by $F_g = m_g g$,where $m_g$ is the gravitational mass and $g$ is the acceleration due to gravit

Vedclass · Accepted Answer

Same weight but different acceleration due to gravity

Vedclass · Answer

(A) The gravitational force acting on a body is given by $F_g = m_g g$,where $m_g$ is the gravitational mass and $g$ is the acceleration due to gravity. The weight of the body is equal to this gravitational force,so $W = m_g g$.Since the gravitational mass $m_g$ is the same for both bodies,their weight $W$ will be the same.According to Newton's second law,$F = m_i a$,where $m_i$ is the inertial mass and $a$ is the acceleration. Equating the gravitational force to the inertial force,we get $m_g g = m_i a$.Thus,the acceleration is $a = (m_g / m_i) g$.Since the gravitational mass $m_g$ is the same but the inertial mass $m_i$ is different for the two bodies,the acceleration $a$ will be different for the two bodies.Therefore,the bodies will have the same weight but different acceleration due to gravity.

The ratio of inertial mass and gravitational mass has been found to be $1$ for all material bodies. If this ratio were different for different bodies,what would be the consequence for two bodies having the same gravitational mass but different inertial masses?

Similar Questions

Three particles $A, B$ and $C$ each of mass $m$ are lying at the corners of an equilateral triangle of side $L$. If the particle $A$ is released keeping the particles $B$ and $C$ fixed,the magnitude of instantaneous acceleration of $A$ is ........

The $SI$ unit of $\frac{G}{g}$ is $(g = \text{acceleration due to gravity}, G = \text{gravitational constant})$

Two point masses $m$ and $4m$ are separated by a distance $d$ on a line. $A$ third point mass $m_0$ is to be placed at a point on the line such that the net gravitational force on it is zero. The distance of that point from the $m$ mass is:

The distance between two objects $A$ and $B$ is $r$. The gravitational force between them is inversely proportional to the square of the distance. If the gravitational force between these two objects were inversely proportional to the fourth power of the distance,find the acceleration of object $A$.

Two spheres of masses $m$ and $M$ are situated in air and the gravitational force between them is $F$. The space around the masses is now filled with a liquid of specific gravity $3$. The gravitational force between the bodies will now be

Vedclass Test Series

Exam Paper Generator

Online Exam Module