Give one example each of central force and non-central force.
Example of central force Gravitational force, electrostatic force etc.
Example of non-central force Nuclear force, magnetic force acting between two current carrying loops etc.
Draw areal velocity versus time graph for mars.
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).
What is the direction of areal velocity of the earth around the sun?
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.
How is the gravitational force between two point masses affected when they are dipped in water keeping the separation between them the same?
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.
Is it possible for a body to have inertia but no weight?
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.