(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

$A$ research satellite of mass $200 \,kg$ circles the earth in an orbit of average radius $3R/2$,where $R$ is the radius of the earth. Assuming the gravitational pull on a mass of $1 \,kg$ on the earth's surface to be $10 \,N$,the pull on the satellite will be ........ $N$.

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$A$ body has weight $W$ newton at the surface of the earth. Its weight at a height equal to half the radius of the earth will be:

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The force of gravity is least at:

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The diameters of two planets are in the ratio $4 : 1$ and their mean densities in the ratio $1 : 2$. The acceleration due to gravity on the planets will be in the ratio:

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The height above the surface of the earth where acceleration due to gravity becomes $\frac{g}{9}$ is ( $R$ is the radius of the earth,$g$ is the acceleration due to gravity at the surface).

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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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$A$ research satellite of mass $200 \,kg$ circles the earth in an orbit of average radius $3R/2$,where $R$ is the radius of the earth. Assuming the gravitational pull on a mass of $1 \,kg$ on the earth's surface to be $10 \,N$,the pull on the satellite will be ........ $N$.

$A$ body has weight $W$ newton at the surface of the earth. Its weight at a height equal to half the radius of the earth will be:

The force of gravity is least at:

The diameters of two planets are in the ratio $4 : 1$ and their mean densities in the ratio $1 : 2$. The acceleration due to gravity on the planets will be in the ratio:

The height above the surface of the earth where acceleration due to gravity becomes $\frac{g}{9}$ is ( $R$ is the radius of the earth,$g$ is the acceleration due to gravity at the surface).

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