
An electric motor creates a tension of 4500N in a hoisting cable and reels it in at the rate of $2m{s^{ - 1}}$. What is the power of the electric motor?
A) $15kW$
B) $9kW$
C) $225kW$
D) $9000HP$
Answer
125.4k+ views
Hint: An electric motor is a rotating device that converts electrical energy into mechanical energy. The power of the electric motor is the force that it applies on the cable or the tension it generates times the velocity or rate at which it pulls it in. It can be calculated using a simple formula. Make sure to convert everything in S.I. units.
Formulae used:
$P = F \times v$
Where $P$ is the power of the electric motor, $F$ is the force or tension in cable and $v$ is the velocity of rate at which the cable is reeled in.
Complete step by step solution:
An electric motor is based on the principle that a current carrying coil placed in a magnetic field experiences some form of a torque. This constant generation of torque gives rise to mechanical energy in the motor that can be used to, in cases like this, hoist a cable and reel it in to reduce the strain on an individual.
The power required in such cases is calculated by the formula;
$P = F \times v$
Where $P$ is the power of the electric motor, $F$ is the force or tension in cable and $v$ is the velocity of rate at which the cable is reeled in.
Here $F = 4500N$ and $v = 2m{s^{ - 1}}$
Therefore,
$P = F \times v$
$ \Rightarrow P = 4500 \times 2$
$ \Rightarrow P = 9000Nm{s^{ - 1}}$
$ \Rightarrow P = 9000W$
$ \Rightarrow P = 9kW$
Therefore the power of the electric motor is $9kW$ which is option (B).
Note: In an electric motor, both emf and current are generated. This is largely responsible for the power of the motor and the power can also be calculated with respect to the current and resistance, had the following been provided in the question. Since only force and velocity were mentioned in the question, we have to use this formula.
Formulae used:
$P = F \times v$
Where $P$ is the power of the electric motor, $F$ is the force or tension in cable and $v$ is the velocity of rate at which the cable is reeled in.
Complete step by step solution:
An electric motor is based on the principle that a current carrying coil placed in a magnetic field experiences some form of a torque. This constant generation of torque gives rise to mechanical energy in the motor that can be used to, in cases like this, hoist a cable and reel it in to reduce the strain on an individual.
The power required in such cases is calculated by the formula;
$P = F \times v$
Where $P$ is the power of the electric motor, $F$ is the force or tension in cable and $v$ is the velocity of rate at which the cable is reeled in.
Here $F = 4500N$ and $v = 2m{s^{ - 1}}$
Therefore,
$P = F \times v$
$ \Rightarrow P = 4500 \times 2$
$ \Rightarrow P = 9000Nm{s^{ - 1}}$
$ \Rightarrow P = 9000W$
$ \Rightarrow P = 9kW$
Therefore the power of the electric motor is $9kW$ which is option (B).
Note: In an electric motor, both emf and current are generated. This is largely responsible for the power of the motor and the power can also be calculated with respect to the current and resistance, had the following been provided in the question. Since only force and velocity were mentioned in the question, we have to use this formula.
Recently Updated Pages
JEE Main 2021 July 20 Shift 2 Question Paper with Answer Key

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

JEE Main 2021 July 25 Shift 2 Question Paper with Answer Key

JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility & More

Class 11 JEE Main Physics Mock Test 2025

JEE Main Exam Marking Scheme: Detailed Breakdown of Marks and Negative Marking

JEE Main 2023 January 24 Shift 2 Question Paper with Answer Keys & Solutions

Learn About Angle Of Deviation In Prism: JEE Main Physics 2025

JEE Main 2025: Conversion of Galvanometer Into Ammeter And Voltmeter in Physics

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements

NCERT Solutions for Class 11 Physics Chapter 9 Mechanical Properties of Fluids

Units and Measurements Class 11 Notes: CBSE Physics Chapter 1

NCERT Solutions for Class 11 Physics Chapter 2 Motion In A Straight Line

Important Questions for CBSE Class 11 Physics Chapter 1 - Units and Measurement
