A person carries a bucket of water of mass 20 kg for a distance of 10 m. Calculate the work done.

• Mass of the bucket ($m$) = $20 \text{ kg}$
• Distance ($d$) = $10 \text{ m}$
• Acceleration due to gravity ($g$) = $9.8 \text{ m/s}^2$ (standard value)

In physics, work done ($W$) is calculated as the product of the force applied and the displacement in the direction of the force ($W = F \cdot d \cdot \cos(\theta)$).

If a person carries a bucket horizontally, the force exerted by the person to support the bucket is upwards (against gravity), while the displacement is horizontal. In this case, the angle ($\theta$) between the force and displacement would be $90^\circ$, and since $\cos(90^\circ) = 0$, the mechanical work done by the supporting force would be $0 \text{ J}$.

However, since $0 \text{ J}$ is not among the options and the options are non-zero, this question likely implies the work done against gravity if the bucket were lifted by the given distance. This is a common interpretation in such problems when the phrasing is ambiguous. We will assume the "distance of $10 \text{ m}$" refers to a vertical displacement against gravity.

The force required to lift the bucket is its weight, $F = mg$.
The work done ($W$) to lift an object against gravity is:

Using the given distance as the height ($h$):

This matches one of the provided options.

The final answer is $\text{1960 J}$.