Q.A hemispherical shell of uniform mass density is oriented like a bowl, with its flat circular face horizontal and on top and its curved surface bulging downward. Let $C$ be the centre of the flat circular face. Choose the correct alternative for the direction of the gravitational intensity (gravitational field) at the centre $C$.

Gravitational Field Direction: From Intuition to Precision

Imagine you're holding a ball in your hand. The moment you let go, it falls straight down toward the floor. Not sideways, not up — straight down. That "down" direction is the direction of the gravitational field at that point.

Now picture yourself on the other side of the Earth — in Australia, for instance. If you drop a ball there, it also falls "down" — but from your perspective, that "down" is toward the ground beneath your feet, which points toward the centre of the Earth. So the direction of the gravitational field is always toward the centre of the Earth.

This is the core intuition: gravity pulls things toward the source of the field.

The Precise Statement

Mathematically, if you place a test mass $m$ at a position $\vec{r}$ relative to a source mass $M$, the gravitational field $\vec{g}$ at that point is:

Here:

• $\hat{r}$ is a unit vector pointing away from $M$ (radially outward).
• The minus sign flips that direction: the field points toward $M$ (radially inward).

So the direction of $\vec{g}$ is always toward the source mass.

Why "Toward the Source"?

Think of a single massive object — say, the Sun. A small rock anywhere near the Sun feels a pull straight toward the Sun's centre. If you place the rock to the left of the Sun, it gets pulled right. If you place it above, it gets pulled down. The pull is always along the line connecting the rock to the Sun's centre, and it always points toward the Sun.

This is because gravity is a central force — it acts along the line joining two masses, and it's always attractive. There's no repulsive gravity.

What About Multiple Masses?

If you have two or more masses (like the Earth and the Moon), the net gravitational field at a point is the vector sum of the fields from each mass. The direction of the net field is the direction of that sum — it points toward the combined effective centre of all the masses, weighted by their distances and sizes.

For example, on the surface of the Earth, the Moon's gravity also pulls on you, but it's much weaker than Earth's. So the net field points almost exactly toward Earth's centre, with a tiny tilt toward the Moon.

A Common Misconception …