Question 183: Gravitation

Question

Consider two solid spheres of radii R
1
= 1m,
R
2
= 2m and masses M
1
and M
2
, respectively.
The gravitational field due to sphere (1) and (2) are shown. The value of $${{{M_1}} \over {{M_2}}}$$ is :

Accepted Answer

Gravitational field on the surface of a solid
sphere
E = $${{GM} \over {{R^2}}}$$
By the graph
E
1
= $${{G{M_1}} \over {R_1^2}}$$
and E
2
= $${{G{M_2}} \over {R_2^2}}$$
$$ 	herefore $$ $${{{E_1}} \over {{E_2}}} = {\left( {{{{R_2}} \over {{R_1}}}} ight)^2}\left( {{{{M_1}} \over {{M_2}}}} ight)$$
$$ \Rightarrow $$ $${2 \over 3} = {\left( {{2 \over 1}} ight)^2}\left( {{{{M_1}} \over {{M_2}}}} ight)$$
$$ \Rightarrow $$ $${{{{M_1}} \over {{M_2}}}}$$ = $${1 \over 6}$$

Answer

$${2 \over 3}$$

Answer

$${1 \over 6}$$

Answer

$${1 \over 2}$$

Answer

$${1 \over 3}$$

Gravitation

Consider two solid spheres of radii R 1 = 1m, R 2 = 2m and masses M 1 and M 2 , respectively. The gravitational field due to sphere (1) and (2) are shown. The value of ${{{M_1}} \over {{M_2}}}$ is :

Choose the correct answer: