Final answer:
The work done in moving a block across a rough surface and the heat energy gained by the block are both measured in Joules (J), the unit of work and energy in the International System of Units (SI). Therefor, the correct option is 3.
Step-by-step explanation:
The work done in moving a block across a rough surface and the heat energy gained by the block can both be measured in Joules (J). This is because the definition of work and energy in physics involves the application of a force over a distance. For the work done, this is calculated as the force times the displacement caused by the force in the direction of the force. Heat energy transferred to an object, which may also be represented by the amount of work done, is likewise measured in Joules, as established by the mechanical equivalent of heat. Work and energy are quantified in the International System of Units (SI) using the term joule, which is effectively a newton-meter (1 N·m). A single Joule is equivalent to the amount of energy required to apply a force of 1 newton over a distance of 1 meter (1 kg·m²/s²). In summary, when a block has heat energy transferred due to friction with a rough surface, this energy can be regarded as having been done via work against friction. Therefore, both the work done on the block in moving it and the heat energy it gains are measured in the same unit, Joules (J).