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-I:
For a mass M kept at the centre of a cube of side ' a ', the flux of gravitational field passing through its sides is .
and
Statement - II
If the direction of a field due to a point source is radial and its dependence on the distance ' ' for the source is given as , 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
Statement-I:
For a mass M kept at the centre of a cube of side ' a ', the flux of gravitational field passing through its sides is .
and
Statement - II
If the direction of a field due to a point source is radial and its dependence on the distance ' ' for the source is given as , 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
- (A)Statement -1 is false, Statement -2 is true.
- (B)Statement - 1is true, Statement - 2 is true; Statement -2 is correct explanation for Statement-1.✓ Correct
- (C)Statement -1 is true, Statement -2 is true; Statement -2 is not a correct explanation for Statement-1.
- (D)Statement - 1 is true, Statement - 2 is False.
Answer: (B)
Solution
The second statement is simply Gauss's law stated for any field that is radial and falls off as : for such a field the flux through a closed surface depends only on the source enclosed, not on the surface's size or shape. Gravity is exactly such a field, and applying this to a mass at the centre of a cube gives a total flux of magnitude through its faces, which is what the first statement asserts. Both statements are correct, and the general flux principle of the second is precisely the reason the first holds.
JEE Main · 2008 · 27 Apr 2008 · Offline · Single correct option