An automobile engine develops 100 kW when rotating at a speed of 1800 rpm. The torque delivered

Name: Problem 59, Chapter 7: Objective NCERT at your FINGERTIPS: Physics
Uploaded: 2021-09-28T14:28:46-08:00
Duration: 1 min 47 s
Channel: Dheeraj Sharma
Description: An automobile engine develops 100 kW when rotating at a speed of 1800 rpm. The torque delivered by the engine is (a) (10^2)/(6 π) N m (b) (10^4)/(6 π) Nm (c) (10^6)/(6 π) N m (d) (10^8)/(6 π) N m

step 1 In this question we have given that an automobile engine develops 100 kilowatt power when it rot

Question

An automobile engine develops $100 \mathrm{~kW}$ when rotating at a speed of $1800 \mathrm{rpm}$. The torque delivered by the engine is (a) $\frac{10^{2}}{6 \pi} \mathrm{N} \mathrm{m}$ (b) $\frac{10^{4}}{6 \pi} \mathrm{Nm}$ (c) $\frac{10^{6}}{6 \pi} \mathrm{N} \mathrm{m}$ (d) $\frac{10^{8}}{6 \pi} \mathrm{N} \mathrm{m}$

   An automobile engine develops $100 \mathrm{~kW}$ when rotating at a speed of $1800 \mathrm{rpm}$. The torque delivered by the engine is
(a) $\frac{10^{2}}{6 \pi} \mathrm{N} \mathrm{m}$
(b) $\frac{10^{4}}{6 \pi} \mathrm{Nm}$
(c) $\frac{10^{6}}{6 \pi} \mathrm{N} \mathrm{m}$
(d) $\frac{10^{8}}{6 \pi} \mathrm{N} \mathrm{m}$

Objective NCERT at your FINGERTIPS: Physics

NCERT 11th Edition

Chapter 7, Problem 59

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Solved by Expert Dheeraj Sharma

09/28/2021

Step 1

Step 1: We are given that the power developed by the engine is $100 \mathrm{~kW}$, which is equal to $10^{5} \mathrm{~W}$. Show more…

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An automobile engine develops $100 \mathrm{~kW}$ when rotating at a speed of $1800 \mathrm{rpm}$. The torque delivered by the engine is (a) $\frac{10^{2}}{6 \pi} \mathrm{N} \mathrm{m}$ (b) $\frac{10^{4}}{6 \pi} \mathrm{Nm}$ (c) $\frac{10^{6}}{6 \pi} \mathrm{N} \mathrm{m}$ (d) $\frac{10^{8}}{6 \pi} \mathrm{N} \mathrm{m}$

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Key Concepts

Angular Velocity Conversion

Angular velocity, typically given in radians per second, is often provided in revolutions per minute (rpm) in practical contexts. Converting rpm to rad/s involves using the factor (2? / 60), which allows the integration of rotational speed into the power-torque formula correctly.

Power and Torque Relationship

In rotational dynamics, power is directly related to torque and angular velocity by the formula P = ??, where P is power, ? is torque, and ? is angular velocity. This relationship is fundamental for understanding how an engine's rotational force (torque) contributes to its overall power output.

Unit Consistency and Dimensional Analysis

Ensuring that units are consistent is critical in physics problems. The units must be properly converted (e.g., kilowatts to watts, rpm to rad/s) so that the mathematical relationships between quantities such as power, torque, and angular velocity remain valid and yield accurate results.

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