(A) For a particle of mass $m$ at a distance $r$ $(r < R_e)$ from the center of the Earth,the gravitational force is due only to the mass $M'$ of the

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(A) For a particle of mass $m$ at a distance $r$ $(r The mass $M'$ of the sphere of radius $r$ is given by: $M' = \rho \cdot V = \left( \frac{M_e}{\frac{4}{3} \pi R_e^3} \right) \cdot \left( \frac{4}{3} \pi r^3 \right) = M_e \frac{r^3}{R_e^3}$.The gravitational force $F$ on the particle is: $F = \frac{G M' m}{r^2}$.Substituting the value of $M'$: $F = \frac{G (M_e \frac{r^3}{R_e^3}) m}{r^2} = \frac{G M_e m r^3}{R_e^3 r^2} = \frac{G M_e m}{R_e^3} r$.

Class 11 Physics Gravitation Acceleration Due to Gravity and its Variation

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$A$ tunnel is dug along a diameter of the Earth. If $M_e$ and $R_e$ are the mass and radius of the Earth respectively,then the force on a particle of mass $m$ placed in the tunnel at a distance $r$ from the center is:

A
$\frac{G M_e m}{R_e^3} r$
B
$\frac{G M_e}{R_e^3} \cdot \frac{m}{r}$
C
$\frac{G M_e m}{r} R_e^3$
D
$\frac{G M_e m}{R_e^2} r$

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Acceleration Due to Gravity and its Variation

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$A$ tunnel is dug along a diameter of the Earth. If $M_e$ and $R_e$ are the mass and radius of the Earth respectively,then the force on a particle of mass $m$ placed in the tunnel at a distance $r$ from the center is:

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