
A pulley system has a velocity ratio of 2 and efficiency $80\,\% $ . calculate mechanical advantage
(A) 2.4
(B) 1.6
(C) 2
(D) 2.2
Answer
146.7k+ views
Hint: We will calculate the mechanical advantage of a pulley using the formula $MA = VA \times \eta $ formula. Here, MA is mechanical advantage, VA is velocity ratio and $\eta $ is efficiency.
Complete step by step answer
It is advantageous when friction is not present. When a force is applied to a pulley; the fraction by which the machine changes is known as mechanical advantage.
Ideal machine efficiency is greater than actual machines used in the real world. As the number of ropes increases less amount of mechanical work is needed to do work. As the number of rope required to pull the system is 1, then the ideal mechanical advantage of a single fixed pulley will be 1. Similarly, when 2 ropes are used to pull the load, then ideal mechanical work is 2.
We are given that velocity ratio I.e ratio of speed with which the rope is pulled is given in ratio 3
Efficiency is $80\,\% $.
It is defined as the ratio of output to input multiplied by 100.
$\eta = 0.8$
Mechanical advantage of system
$MA = VA \times \eta $
$MA = 3 \times 0.8$
$MA = 2.4$
Hence 2.4 is the mechanical advantage of the system. Option A is correct.
Note
If efficiency used is 80 instead of 0.8 then we will get a wrong solution. This is because efficiency is output to input ratio multiplied by 100. therefore, it should be divided by 100. Secondly, ideal mechanical work cannot be less than actual mechanical work.
There is no unit in mechanical advantage that is a unit-less quantity.
Complete step by step answer
It is advantageous when friction is not present. When a force is applied to a pulley; the fraction by which the machine changes is known as mechanical advantage.
Ideal machine efficiency is greater than actual machines used in the real world. As the number of ropes increases less amount of mechanical work is needed to do work. As the number of rope required to pull the system is 1, then the ideal mechanical advantage of a single fixed pulley will be 1. Similarly, when 2 ropes are used to pull the load, then ideal mechanical work is 2.
We are given that velocity ratio I.e ratio of speed with which the rope is pulled is given in ratio 3
Efficiency is $80\,\% $.
It is defined as the ratio of output to input multiplied by 100.
$\eta = 0.8$
Mechanical advantage of system
$MA = VA \times \eta $
$MA = 3 \times 0.8$
$MA = 2.4$
Hence 2.4 is the mechanical advantage of the system. Option A is correct.
Note
If efficiency used is 80 instead of 0.8 then we will get a wrong solution. This is because efficiency is output to input ratio multiplied by 100. therefore, it should be divided by 100. Secondly, ideal mechanical work cannot be less than actual mechanical work.
There is no unit in mechanical advantage that is a unit-less quantity.
Recently Updated Pages
How to find Oxidation Number - Important Concepts for JEE

How Electromagnetic Waves are Formed - Important Concepts for JEE

Electrical Resistance - Important Concepts and Tips for JEE

Average Atomic Mass - Important Concepts and Tips for JEE

Chemical Equation - Important Concepts and Tips for JEE

Concept of CP and CV of Gas - Important Concepts and Tips for JEE

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

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

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

JEE Main Participating Colleges 2024 - A Complete List of Top Colleges

Degree of Dissociation and Its Formula With Solved Example for JEE

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

JEE Advanced 2025: Dates, Registration, Syllabus, Eligibility Criteria and More

Units and Measurements Class 11 Notes: CBSE Physics Chapter 1

NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements

Motion in a Straight Line Class 11 Notes: CBSE Physics Chapter 2

JEE Advanced Weightage 2025 Chapter-Wise for Physics, Maths and Chemistry
