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Answer :
Final answer:
A shaft with a diameter of 0.51 inches would be able to support approximately 396 N·m of torque. Therefore, c)396 N·m is correct option.
Explanation:
The torque exerted by a shaft is proportional to its diameter. Therefore, if a shaft with a diameter of 0.26 inches is able to support 102 ft-lb of torque, a shaft with a diameter of 0.51 inches would be able to support a proportional amount of torque. To calculate the torque, we can use the formula:
Torque = Force x Distance
Since the force is directly proportional to the diameter, we can use the following ratio to find the new torque:
Torque(new) = (Diameter(new) / Diameter(old)) x Torque(old)
Plugging in the values, we get:
Torque(new) = (0.51 inches / 0.26 inches) x 102 ft-lb
Converting the result to N·m, we get:
Torque(new) = (0.51 inches / 0.26 inches) x 138 N·m ≈ 396 N·m
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