The variation of acceleration due to gravity | vedclass

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(B) The acceleration due to gravity $g$ varies with the distance $d$ from the centre of the Earth as follows:$1$. Inside the Earth $(d < R)$:The accel

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(B) The acceleration due to gravity $g$ varies with the distance $d$ from the centre of the Earth as follows:$1$. Inside the Earth $(d The acceleration due to gravity at a distance $d$ from the centre is given by $g_d = \frac{GMd}{R^3} = g \frac{d}{R}$,where $g$ is the acceleration due to gravity at the surface. This shows that $g_d \propto d$,which is a linear relationship.$2$. At the surface of the Earth $(d = R)$:The acceleration due to gravity is maximum,$g = \frac{GM}{R^2}$.$3$. Outside the Earth $(d > R)$:The acceleration due to gravity at a distance $d$ from the centre is given by $g_d = \frac{GM}{d^2}$. This shows that $g_d \propto \frac{1}{d^2}$,which is an inverse square relationship.Combining these,the graph starts from the origin $(d=0, g=0)$,increases linearly to a maximum at $d=R$,and then decreases following an inverse square curve for $d > R$. This corresponds to the graph shown in option $B$.

The variation of acceleration due to gravity $g$ with distance $d$ from the centre of the earth is best represented by ($R =$ Earth's radius)

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