Areal velocity of a planet revolving around the sun is constant with time. Therefore, graph between areal velocity and time is a straight line (AB) parallel to time axis. (Kepler's second law).

Areal velocity of the earth around the sun is given by

$$\frac{d \mathrm{~A}}{d t}=\frac{\mathrm{L}}{2 m}$$

where, $$\mathbf{L}$$ is the angular momentum and $$m$$ is the mass of the earth.

But angular momentum $$\quad L=r\times p=r\times mv$$

$$\therefore$$ Areal velocity $$\quad \left(\frac{d A}{d t}\right)=\frac{1}{2 m}(\mathrm{r} \times m \mathrm{v})=\frac{1}{2}(\mathrm{r} \times \mathrm{v})$$

Therefore, the direction of areal velocity $$\left(\frac{d \mathrm{~A}}{d t}\right)$$ is in the direction of $$(\mathrm{r} \times \mathrm{v})$$, i.e., perpendicular to the plane containing $$r$$ and $$v$$ and directed as given by right hand rule.

Gravitational force acting between two point masses $$m_1$$ and $$m_2, F=\frac{G m_1 m_2}{r^2}$$, is independent of the nature of medium between them. Therefore, gravitational force acting between two point masses will remain unaffected when they are dipped in water.

Yes, a body can have inertia (i.e., mass) but no weight. Everybody always have inertia (i.e., mass) but its weight $(\mathrm{mg})$ can be zero, when it is taken at the centre of the earth or during free fall under gravity.

e.g., In the tunnel through the centre of the earth, the object moves only due to inertia at the centre while its weight becomes zero.

A body cannot be shielded from the gravitational influence of nearby matter, because gravitational force between two point mass bodies is independent of the intervening medium between them.

It is due to the above reason, we cannot shield a body from the gravitational influence of nearby matter by putting it either inside a hollow sphere or by some other means.