Final answer:
The mass that can be supported by a new beam with a breadth of 6 cm and a length of 40 m is calculated to be 450 kg, which does not match any of the provided options.
Step-by-step explanation:
The situation described in the question involves a beam that supports a certain mass. According to the details, the beam's capability to support mass varies directly with the breadth (b) and inversely with the length (l). The given beam's parameters allow it to support a 400 kg mass with a breadth of 4 cm and a length of 30 m. To find the mass that can be supported by a new beam with a breadth of 6 cm and a length of 40 m, we use the principle of direct and inverse relations:
Let M1 and M2 represent the masses supported by the first and second beams respectively, b1 and b2 represent their breadths, and l1 and l2 their lengths. Hence, we have the proportionality: M1/M2 = (b1*l2) / (b2*l1).
Substituting known values gives M2 = (M1*b2*l1) / (b1*l2) = (400 kg * 6 cm * 30 m) / (4 cm * 40 m). Upon calculation, M2 = 450 kg.
Unfortunately, none of the options provided (a) 2000 kg, (b) 3000 kg, (c) 2500 kg, (d) 3500 kg matches the calculated value of 450 kg, which suggests there might be a mistake in the question's options or perhaps a miscalculation in the process. Based on the information, a correct answer cannot be matched to the given options.