Suppose the gravitational mass,m_G,and inertial mass,m_I,were not equivalent and 1m_G = 2 m_I.Near Earth's surface,the acceleration due to gravity would have a value of A)4.905 m/s² B)9.81 m/s² C)14.7 m/s² D)19.62 m/s² E)24.53 m/s²

Question

Quizplus · Accepted Answer

The acceleration due to gravity is calculated using the formula $a = \frac{F}{m_{I}}$, where $F = G \frac{m_{E}m_{G}}{r^2}$ and $m_{I}$ is the inertial mass. If $m_{G} = 2m_{I}$, then $a = G \frac{m_{E}2m_{I}}{r^2} \cdot \frac{1}{m_{I}} = 2g$, where $g = 9.81 m/s^2$ is the standard acceleration due to gravity. Thus, $a = 2 \times 9.81 m/s^2 = 19.62 m/s^2$. However, since the question implies a direct relationship between gravitational and inertial mass that contradicts this setup, and no option matches the calculated value, the premise of the question suggests a misunderstanding. Given the standard understanding that gravitational and inertial masses are equivalent, and without altering the fundamental laws of physics, the acceleration due to gravity remains $9.81 m/s^2$, making all provided options incorrect based on the calculation. However, the question's premise itself is flawed as it contradicts the equivalence principle, which is a cornerstone of general relativity, stating that gravitational and inertial masses are equivalent. This principle ensures that the acceleration due to gravity is constant and equal to $9.81 m/s^2$ near Earth's surface, not altered by hypothetical differences between gravitational and inertial mass.

Suppose the Gravitational Mass,mG,and Inertial Mass,mI,were Not Equivalent and 1mG

Suppose the Gravitational Mass,m_G,and Inertial Mass,m_I,were Not Equivalent and 1m_G