Final answer:
To balance the 1380 kg truck on an incline, assuming an ideal frictionless scenario and a simple pulley system, the mass (m) of the counterweight would need to be equal to the mass of the truck, which is 1380 kg.
Step-by-step explanation:
To determine the mass (m) of the counterweight needed to balance a 1380 kg truck on an incline, we can use the principles of static equilibrium. Assuming a frictionless scenario, and neglecting pulley mass, the mass of the counterweight does not necessarily have to be equal to the truck's mass. The actual required mass would depend on the angle of the incline and the setup of the pulley system. Mathematically, this can be determined by calculating the forces acting along the inclined plane and setting them to be equal since it's in static equilibrium.
However, the information provided here does not allow for a precise calculation because the angle of the incline and details of the pulley system are not given. Therefore, assuming a symmetrical setup with equal angles and a single pulley system, the force needed to balance the truck would simply be its weight (mass times gravity). Therefore, the counterweight would need to exert an equal force, giving us answer choice (B): The mass (m) of the counterweight is equal to the mass of the truck (1380 kg).