Q.15 Physics ⭐ 360° Option Elimination Active

NEET 2021 Physics Question 15 Solution

Topic: Work, Energy and Power · Official NTA Booklet Code M1

Question

Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of the input energy. How much power is generated by the turbine? (g = 10 m/s²)

✓

Verified Against NTA Final Answer Key

Option (2) : 8.1 kW

📚 Work, Energy and Power Easy

📋 Given Parameters & Problem Setup

Height of Fall (h) 60 m

Rate of Water Flow (dm/dt) 15 kg/s

Frictional Loss 10% of input energy

Acceleration Due to Gravity (g) 10 m/s^2

⚡

The 30-Second Exam Hall Shortcut: ⚡ Input Power × 90% Efficiency

⏱️ Save ~20 seconds

$P_{\text{in}} = \frac{dm}{dt} g h = 15 \times 10 \times 60 = 9000\text{ W} = 9\text{ kW}$ . Efficiency is $100\% - 10\% = 90\%$ . Generated power $P_{\text{out}} = 0.9 \times 9\text{ kW} = 8.1\text{ kW}$ ! Instant 15-second calculation matching Option (2)!

1 Compute total gravitational input power:

P_{\text{in}} = \left(\frac{dm}{dt}\right) g h

P_{\text{in}} = 15 \times 10 \times 60 = 9000\text{ W} = 9.0\text{ kW}

3 Since 10% is lost to friction, efficiency

\eta = 90\% = 0.90

4 Generated power

P_{\text{out}} = \eta P_{\text{in}} = 0.90 \times 9.0\text{ kW} = 8.1\text{ kW}

5 Match Option (2).

🛡️

Why You Can 100% Trust This Shortcut: Canonical conservation of mechanical energy and hydroelectric turbine efficiency relation.

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Calculating Gravitational Potential Energy Input Rate

Water of mass $\Delta m$ falling from height $h$ carries gravitational potential energy $\Delta U = (\Delta m)gh$ . The rate of potential energy delivered (input power) is:

P_{\text{in}} = \frac{\Delta U}{\Delta t} = \left(\frac{dm}{dt}\right) g h = (15\text{ kg/s}) \times (10\text{ m/s}^2) \times (60\text{ m}) = 9000\text{ W} = 9.0\text{ kW}

Step 2

Accounting for Frictional Energy Losses

Frictional losses account for $10\%$ of the input energy. The remaining $90\%$ is converted into electrical output power by the turbine:

\eta = 100\% - 10\% = 90\% = 0.90

Step 3

Calculating Net Power Generated by the Turbine

Multiply input power by the net efficiency factor:

P_{\text{out}} = \eta P_{\text{in}} = 0.90 \times 9000\text{ W} = 8100\text{ W} = 8.1\text{ kW}

⭐

360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 1

✗ Incorrect

Verdict & Scientific Reason:

Exceeds the 100% ideal input power of 9.0 kW (unphysical).

⚠️

Student Fallacy (Why candidates pick this trap): Adding 10% to input power (

9 + 0.9 = 9.9

10.2

2 2

✓ 100% Correct

Verdict & Scientific Reason:

Exact electrical output power generated: $0.90 \times 9.0\text{ kW} = 8.1\text{ kW}$ .

💡

Why this is airtight: None; textbook power and efficiency computation.

3 3

✗ Incorrect

Verdict & Scientific Reason:

Exceeds available gravitational potential energy.

⚠️

Student Fallacy (Why candidates pick this trap): Multiplication error.

4 4

✗ Incorrect

Verdict & Scientific Reason:

Incorrect subtraction of losses.

⚠️

Student Fallacy (Why candidates pick this trap): Subtracting 2 kW arbitrarily.

⚠️

NTA Trap Alert: Gross Input vs. Net Generated Power Trap

Students who compute $P = 9.0\text{ kW}$ sometimes look for 9.0 kW, and if not present, guess a nearby number without applying the $10\%$ frictional loss reduction factor.

🛡️ How to avoid the -1 mark: Read carefully: "losses are 10% of input energy". Multiply

P_{\text{in}}

0.90

📖

Core NEET Syllabus Standard

NCERT Physics · Work, Energy and Power Standard Benchmark

Core Scientific Principle Tested:

"Power generated equals rate of energy input multiplied by the efficiency of conversion ( $P_{\text{out}} = \eta P_{\text{in}}$ )."

Syllabus Focus: Power and Efficiency of Machines

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2021 Physics Question 15 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Input Power × 90% Efficiency

Step-by-Step Rigorous Workflow & Mathematical Proof

Calculating Gravitational Potential Energy Input Rate

Accounting for Frictional Energy Losses

Calculating Net Power Generated by the Turbine

360° Option Elimination Engine Key Feature

NTA Trap Alert: Gross Input vs. Net Generated Power Trap

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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