A motor of 1kW power is used to run a pump.If pump raises 100kg of water to h 10m in 5s.Efficiency?

Ajouté : 2026-05-09

[00:00:00]The question is, a motor of 1 kW power is used to run a pump. If pump is rises the 100 kg of water to height of 10 m in 5 seconds, what is the efficiency of a motor? Take g equals to 10 m/s squared.

[00:00:17]In the given question, if you observe it properly, they have what they have mentioned here.

[00:00:23]They have given the power of a motor is 1 kW.

[00:00:28]And also they have mentioned 100 kg of water is raised to 10 m for 5 seconds and the g value is given.

[00:00:36]So, it is a power generated question and already they have asked here. In the question, they have mentioned it is the efficiency of this motor is they are asking the efficiency also.

[00:00:47]So, what we have to find how to find the efficiency. Efficiency or eta to find, we have to go with the formula power output divided by power input.

[00:01:02]And if you want to find the percentage of it, then you have to multiply the 100.

[00:01:06]Okay, that is the efficiency formula to find the answer. So, we must know here what is the power input.

[00:01:14]Okay, power in I will write.

[00:01:16]And what is the power output? Both we must know. So, if you want to find the power in, in the question they have given that power is 1 kW, which means that 1 kW.

[00:01:30]It is nothing but 1,000 W of power input. What about the power output? How to find the power output? Then you have to read the question.

[00:01:39]What they have given in the question?

[00:01:40]They have mentioned that the pump rises 100 kg of water at a height of 10 m in 5 seconds. Which means that this 100 kg of water is act as a mass.

[00:01:55]They have given the mass as 100 kg.

[00:01:58]And also they have given the height is 10 m. It is the water is raising 10 m and the time is given as 5 seconds. And also they have mentioned the g value is 10 m/s squared. By the given things, you will understand what actually is what is the power output. See, there's a water here in the ground level which is 10 100 kg of water. It is raising for a 10 m above the ground and the water is to pump this, it will take only 5 seconds.

[00:02:26]It is rare case. Why it is rare case?

[00:02:29]Later on, I will explain to you.

[00:02:32]So, this is the actual procedure what is going on. So, how to find the power output? The power output going to be equals to what is the work done.

[00:02:43]So, okay? So, we will find the power output later. First, we have to find what is the work done.

[00:02:48]So, work done by the machine will be equals to the water is raised, so it is a potential energy.

[00:02:55]The water is raised for a 10 m, so that much work is done by the motor. So, here work done is very important. So, power output formula is work done by time.

[00:03:07]Okay, work done by time. So, we must know what is work done.

[00:03:10]So, work done is nothing but potential energy to raise the water from the zero ground level to the 10 m. So, what is the potential energy formula? mgh. m value is 100 kg.

[00:03:23]g is also given as 10 m/s squared. And the height is 10 m. Everything is in terms of 10s, 100s only. So, if you multiply, there is four zeros, so it is 10,000 joules of work done by the motor to raise that 100 kg. This is the work done, w.

[00:03:43]So, we have to find the power output now. How to find the power output?

[00:03:47]Same formula what I discussed here.

[00:03:50]Work done by time taken. Work done is 10,000 joule.

[00:03:54]The time taken is 5 seconds. That's all.

[00:03:57]So, it is a rare case I said because it you can observe here. If you divide it, you will come to know it is 2,000 W is the power output.

[00:04:08]Why it is inconsistent? Why because the power input, if you observe, power input is 1,000 W and the power output 2,000 W.

[00:04:18]It is normally it is not possible.

[00:04:21]Because your power output must be less than 1,000.

[00:04:25]It is more than 1,000, which means that efficiency of that motor motor is more.

[00:04:30]So, what is the efficiency now?

[00:04:33]Efficiency or eta equals to power output divided by power input into 100. If you are finding percentage, so power output is 2,000 divided by power input is 1,000 into 100.

[00:04:53]If you simplify, zeros will get cancelled. 2 into 100 is 200%.

[00:04:59]So, efficiency cannot be more than 100%.

[00:05:03]So, I said in the beginning only, it is a rare case.

[00:05:07]Okay, it is inconsistent data what they have mentioned. Okay? It It is [snorts] a your conceptual knowledge to check. Yes, the answer is 200%. The efficiency of the motor is 200%, but in real life it is not possible. Thank you.