Question 232: Gravitation

Question

This question contains Statement - $$1$$ and Statement - $$2$$. of the four choices given after the statements, choose the one that best describes the two statements.
Statement - $$1$$:
For a mass $$M$$ kept at the center of a cube of side $$'a'$$, the flux of gravitational field passing through its sides $$4\,\pi \,GM.$$ 
Statement - 2:
If the direction of a field due to a point source is radial and its dependence on the distance $$'r'$$ from the source is given as $${1 \over {{r^2}}},$$ its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface.

Accepted Answer

Gravitational field $$\overrightarrow g $$ = $$ - {{GM} \over {{r^2}}}$$
where, $$M=$$ mass enclosed in the closed surface
Gravitational flux through a closed surface is given by
$${\left| {\overrightarrow g .d\overrightarrow S } \right|}$$ = $$4\pi {r^2}.{{GM} \over {{r^2}}}$$ = $$4\pi GM$$
So Statement - 1 is correct.
Statement - 2 is also correct because when the shape of the earth is spherical, area of the Gaussian surface is $$4\pi {r^2}$$. This proves inverse square law.

Answer

Statement - $$1$$ is false, Statement - $$2$$ is true

Answer

Statement - $$1$$ is true, Statement - $$2$$ is true; Statement - $$2$$ is a correct explanation for Statement - $$1$$

Answer

Statement - $$1$$ is true, Statement - $$2$$ is true; Statement - $$2$$ is not a correct explanation for Statement - $$1$$

Answer

Statement - $$1$$ is true, Statement - $$2$$ is false

Gravitation

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