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/r², its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size o

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 centre of a cube of side $‘ a ’$ , the flux of gravitational field passing through its sides is $4 π G M$ .

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 $\frac{1}{r^{2}}$ , 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.

Smart Achievers · Accepted Answer

(2)

Gravitational field, $E_{g} = - \frac{G M}{r^{2}}$

$Flux, ϕ = \int {\vec{E}}_{g} \cdot d \vec{S} =$ $| E_{g} |$ $4 π r^{2} = - 4 π G M$

Where, M = mass enclosed in the closed surface

This relationship is valid when $| {\vec{E}}_{g} |$ $\propto \frac{1}{r^{2}}$

Solution

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

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

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

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

Ans.
(2)

Gravitational field, $E_{g} = - \frac{G M}{r^{2}}$

$Flux, ϕ = \int {\vec{E}}_{g} \cdot d \vec{S} =$ $| E_{g} |$ $4 π r^{2} = - 4 π G M$

Where, M = mass enclosed in the closed surface

This relationship is valid when $| {\vec{E}}_{g} |$ $\propto \frac{1}{r^{2}}$

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