Machines A, B, and C do the same amount of work, but they each take a different amount of time. Machine A takes more time as compared to machine C. Machine B takes the maximum time to do the same amount of work. Which machine expends the most power doing this work?
A. machine A
B. machine B
C. machine C
D. machines A and B

Machine C expends the most power since it takes the least time to complete the same amount of work compared to Machines A and B. Power is inversely proportional to the time taken when the work done is constant. Therefore, the correct option is machine C.
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Answered by Anonymous | 2025-07-07

Power is the rate at which work is done, defined as P = t W ​ .
Since the work done is the same for all machines, power is inversely proportional to time.
Machine C takes the least time, as t_A > t_C"> t B ​ > t A ​ > t C ​ .
Therefore, machine C expends the most power: machine C ​ .

Explanation

Understanding the Problem We are given that three machines, A, B, and C, do the same amount of work but take different amounts of time. We know that machine A takes more time than machine C, and machine B takes the maximum time. We need to determine which machine expends the most power.

Defining Power Power is defined as the rate at which work is done. Mathematically, this is expressed as: P = t W ​ where:



P is power,
W is work done, and
t is the time taken to do the work.


Relating Power and Time Since all three machines do the same amount of work, W is constant for all of them. Therefore, power is inversely proportional to time. This means that the machine that takes the least time to do the work will expend the most power.

Comparing Time Taken by Each Machine We are given that machine A takes more time than machine C ( t_C"> t A ​ > t C ​ ), and machine B takes the maximum time. This implies t_A"> t B ​ > t A ​ and t_C"> t B ​ > t C ​ . Therefore, we have the relationship: t_A > t_C"> t B ​ > t A ​ > t C ​ This means machine C takes the least time.

Determining Which Machine Expends the Most Power Since machine C takes the least time to do the same amount of work, it expends the most power.

Final Answer Therefore, the machine that expends the most power is machine C.


Examples
Consider a scenario where three different engines are lifting the same weight to the same height. The engine that completes the task in the shortest amount of time is the most powerful, as it delivers energy at a faster rate. This concept is widely used in engineering to compare the efficiency and performance of different machines.

Answered by GinnyAnswer | 2025-07-07