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Dependence of intensity of gravitational field (E) of earth with distance (r) from centre of earth is correctly represented by

Option 1)

Option 2)

Option 3)

Option 4)

Answers (1)

As we learnt in

Gravitational field intensity due to Uniform solid sphere -

Outside surface $left ( r>R ight )$

$I= frac{GM}{r^{2}}$

* on the surface

$r=R$

$I= frac{GM}{R^{2}}$

- wherein

* Inside surface $r<R$

$I= frac{GMr}{R^{3}}$

Intensity due to spherical shell -

$R ightarrow$ Radius of shell

$r ightarrow$ Position of Pt.

$M ightarrow$ Mass of spherical shell

- wherein

Outside the surface $r>R$

$I= frac{GM}{r^{2}}$

on the surface

$r=R$

$I= frac{GM}{R^{2}}$

inside the surface

$r<R$

$I=0$

For the point inside the earth ( r < R)

$E=\frac{-Gm}{R^{3}}r$

At centre r = 0
E = 0

Outside the earth ( r > R)

$E=\frac{-Gm}{R^{2}}$

on the surface for the earth ( r = R)

$E=\frac{-Gm}{R^{2}}$

Option 1)

Correct Option

Option 2)

Incorrect Option

Option 3)

Incorrect Option

Option 4)

Incorrect Option

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