Question 258: Gravitation

Question

A uniform solid sphere of mass ' $m$ ' and radius ' r ' is surrounded by a uniform thin spherical shell of radius ' $2 r$ ' and mass ' $m$ ' then the gravitational field

Accepted Answer

Gravitational field for $\mathrm{x}2 r$,
$$ \mathrm{g}=\frac{2 \mathrm{Gm}}{\mathrm{x}^2} \quad \ldots \ldots\left(\mathrm{~m}_{\mathrm{net}}=\mathrm{m}_{	ext {sphere }}+\mathrm{m}_{	ext {shell }}=2 \mathrm{~m}ight) $$
At a distance of 15 r ,
$$ g=\frac{2 \mathrm{Gm}}{(15 r)^2}=\frac{2}{225} \frac{\mathrm{Gm}}{\mathrm{r}^2} $$
At a distance of 2.5 r ,
$$ \mathrm{g}=\frac{2 \mathrm{Gm}}{(2.5 \mathrm{r})^2}=\frac{2}{6.25} \frac{\mathrm{Gm}}{\mathrm{r}^2}=\frac{8}{25} \frac{\mathrm{Gm}}{\mathrm{r}^2} $$
At a distance of 1.5r,
$$ \mathrm{g}=\frac{\mathrm{Gm}}{(1.5 \mathrm{r})^2}=\frac{1}{2.25} \frac{\mathrm{Gm}}{\mathrm{r}^2}=\frac{4}{9} \frac{\mathrm{Gm}}{\mathrm{r}^2} $$
$	herefore \quad$ The correct option is (B).

Answer

at a distance of 15 r from the centre is
$$ \frac{2}{9} \frac{\mathrm{Gm}}{\mathrm{r}^2} $$

Answer

at a distance of (2.5)r from the centre is
$$ \frac{8}{25} \frac{\mathrm{Gm}}{\mathrm{r}^2} $$

Answer

at a distance of (1.5)r from the centre is zero.

Answer

between the sphere and spherical shell is uniform.

Gravitation

A uniform solid sphere of mass ' m ' and radius ' r ' is surrounded by a uniform thin spherical shell of radius ' 2 r ' and mass ' m ' then the gravitational field

Choose the correct answer: