Answer:
<em>Force of gravity may not affect a pendulum during its equilibrium state</em>. But the gravity can affect the pendulum when a force occurs in any direction of the bob connected to the cord that makes a swing sideways. The gravity of pendulum never stops, it always accelerates. So the gravity affects the pendulum acceleration and speed.
<em>Similarly the tension in the cord will not affect the pendulum</em><em> </em>but if change in the length of the pendulum while keeping other factors constant changes the length of the period of pendulum. longer pendulum swings with lower frequency than shorter pendulums.
Answer:

Explanation:
The work done on the capacitor is equal to the difference in potential energy stored in the capacitor in two different cases.
The potential energy is given by the following formula:

where C can be calculated using the plate separation and area.

Therefore, the potential energy in the first case is

In the second case:

The permittivity of the air is very close to that of vacuum, which is 8.8 x 10^-12.
So, the difference in the potential energy is

I cannot see all the questions, what is 18,19 and 21? (:
Mathematical equations can express dependencies between things, for example the relationship between the speed and acceleration. This can be summarized under "scientific laws".
More complex laws can represent models, for example a model of a human brain on a neuronal level could be based on complex mathematical equations.