The ratio of inertial mass and gravitational | vedclass

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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

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(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?

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