A block of mass $$100$$ kg slides over a distance of $$10$$ m on a horizontal surface. If the co-efficient of friction between the surfaces is $$0.4$$, then the work done against friction (in J) is:

We need to find the work done against friction when a 100 kg block slides 10 m on a horizontal surface with a coefficient of friction of 0.4.

The kinetic friction force on a horizontal surface is:

$$f = \mu m g$$

where $$\mu$$ is the coefficient of friction, $$m$$ is the mass, and $$g$$ is the acceleration due to gravity.

$$f = 0.4 \times 100 \times 10 = 400 \text{ N}$$

(using $$g = 10$$ m/s$$^2$$)

Work done against friction is:

$$W = f \times d = 400 \times 10 = 4000 \text{ J}$$

where $$d = 10$$ m is the distance.

Note: The work done against friction is positive because the friction force opposes the direction of motion. The energy is converted into heat.

The correct answer is Option (3): 4000 J.