The following question contains Statement-1 and Statement-2. Of the four choices given, 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 the gravitational field passing through its sides is 4π GM. Statement-2: If th…

Question

The following question contains Statement-1 and Statement-2. Of the four choices given, 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 the gravitational field passing through its sides is 4π 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/(r²), 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

(3) Statement-1 is true, Statement-2 is true, and Statement-2 is a correct explanation for Statement-1.. Gravity points radially and falls as 1/(r²), which are the two features that make a Gauss type law work at all. That law reads ∮g⃗· dA⃗=-4π GM_enc, so the magnitude of the flux out of any closed surface around M is 4π GM. Neither the side a nor the cube shape enters, so Statement-1 is true. Statement-2 states precisely that shape independence, so it is true and it is the reason Statement-1 holds.

Step-by-step solution

Why the other options are wrong