UPSC Exam > UPSC Notes > Mathematics Optional Notes for UPSC > Generalised coordinate
Generalised coordinate | Mathematics Optional Notes for UPSC PDF Download
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1
Edurev123
Mechanics and Fluid Dynamics
1. Generalised coordinate
1.1 A perfectly rough sphere of mass ?? and radius ?? , rests on the lowest point of
a fixed spherical cavity of radius ?? . To the highest point of the movable sphere is
attached a particle of mass ?? '
and the system is disturbed. Show that the
oscillations are the same as those of a simple pendulum of length
(?? -?? )
?? ?? '
+
?? ?? ?? ?? +?? '
(?? -
?? ?? )
(2009: 30 marks)
Solution:
Now,
?? ?? ''
?=?? ?? ''
???? ?=?? (?? +?? )
(?? -?? )?? ?=??
(?? -?? )???
?=?? ?? ?
Now, total kinetic energy, ?? can be written as
?? =
1
2
?? '
?? ?? 2
+
1
2
?? ?? ????
2
+
1
2
?? ????
?? 2
Now,
Page 2
Edurev123
Mechanics and Fluid Dynamics
1. Generalised coordinate
1.1 A perfectly rough sphere of mass ?? and radius ?? , rests on the lowest point of
a fixed spherical cavity of radius ?? . To the highest point of the movable sphere is
attached a particle of mass ?? '
and the system is disturbed. Show that the
oscillations are the same as those of a simple pendulum of length
(?? -?? )
?? ?? '
+
?? ?? ?? ?? +?? '
(?? -
?? ?? )
(2009: 30 marks)
Solution:
Now,
?? ?? ''
?=?? ?? ''
???? ?=?? (?? +?? )
(?? -?? )?? ?=??
(?? -?? )???
?=?? ?? ?
Now, total kinetic energy, ?? can be written as
?? =
1
2
?? '
?? ?? 2
+
1
2
?? ?? ????
2
+
1
2
?? ????
?? 2
Now,
?? ?? ?=(?? -?? )sin??? ????
?? =(?? -?? )cos??? ·???
?? ?? ?=(?? -?? )cos??? ????
?? =(?? -?? )-sin??? ·???
?? ?? 2
?=???
?? 2
+???
?? 2
=(?? -?? )
2
???
2
?? ????
?=
2
5
?? ?? 2
and ?? =?? ?
?? ?? ?=(?? -?? )sin??? +?? sin??? ???
?? ?=(?? -?? )cos??? ·???
+?? cos??? ·?? ?
?? ?? ?=(?? -?? )cos??? -?? cos??? ???
?? ?=(?? -?? )(-sin??? )·???
+?? sin??? ·?? ?
???
?? 2
+???
?? 2
?=?? ?? 2
=(?? -?? )
2
???
2
+?? 2
?? ?
2
+2(?? -?? )???
?? ?
?? (cos??? cos??? -sin??? sin??? )
?=(?? -?? )
2
???
2
+?? 2
?? ?
2
+2(?? -?? )???
?? ?
(?? ·†
?
-???? )? (ignoring the term ???? as it is very small)
?˜(?? -?? )
2
???
2
+?? 2
?? ?
2
+2(?? -?? )???
?? ?
Now potential energy,
Now lagrange,
?? =-???? (?? -?? )cos??? -?? '
?? {(?? -?? )cos??? -?? cos??? }
?? =?? -?? ?? =
1
2
?? '
{(?? -?? )
2
???
2
+?? 2
???
2
+2(?? -?? )?? ???
?? ?
}+
Take this point as zero potential
As
1
2
?? (?? -?? )
2
???
2
+
1
2
×
2
5
?? ?? 2
?? ?
2
+???? (?? -?? )cos??? +
?? '
?? {(?? -?? )cos??? -?? cos??? }
So, the generalised coordinate will only be one
Convert ?? to ?? .
Also
(?? -?? )???
=?? ?? ?
So,
?? =
1
2
?? '
{?? ?? ?
2
+?? 2
?? ?
2
+2?? 2
???
2
}+
1
2
?? ?? 2
?? ?
2
+
?? ?? 2
5
?? ?
2
+???? (?? -?? )cos??? ?+?? '
?? (?? -?? )cos??? -?? '
???? cos???
Page 3
Edurev123
Mechanics and Fluid Dynamics
1. Generalised coordinate
1.1 A perfectly rough sphere of mass ?? and radius ?? , rests on the lowest point of
a fixed spherical cavity of radius ?? . To the highest point of the movable sphere is
attached a particle of mass ?? '
and the system is disturbed. Show that the
oscillations are the same as those of a simple pendulum of length
(?? -?? )
?? ?? '
+
?? ?? ?? ?? +?? '
(?? -
?? ?? )
(2009: 30 marks)
Solution:
Now,
?? ?? ''
?=?? ?? ''
???? ?=?? (?? +?? )
(?? -?? )?? ?=??
(?? -?? )???
?=?? ?? ?
Now, total kinetic energy, ?? can be written as
?? =
1
2
?? '
?? ?? 2
+
1
2
?? ?? ????
2
+
1
2
?? ????
?? 2
Now,
?? ?? ?=(?? -?? )sin??? ????
?? =(?? -?? )cos??? ·???
?? ?? ?=(?? -?? )cos??? ????
?? =(?? -?? )-sin??? ·???
?? ?? 2
?=???
?? 2
+???
?? 2
=(?? -?? )
2
???
2
?? ????
?=
2
5
?? ?? 2
and ?? =?? ?
?? ?? ?=(?? -?? )sin??? +?? sin??? ???
?? ?=(?? -?? )cos??? ·???
+?? cos??? ·?? ?
?? ?? ?=(?? -?? )cos??? -?? cos??? ???
?? ?=(?? -?? )(-sin??? )·???
+?? sin??? ·?? ?
???
?? 2
+???
?? 2
?=?? ?? 2
=(?? -?? )
2
???
2
+?? 2
?? ?
2
+2(?? -?? )???
?? ?
?? (cos??? cos??? -sin??? sin??? )
?=(?? -?? )
2
???
2
+?? 2
?? ?
2
+2(?? -?? )???
?? ?
(?? ·†
?
-???? )? (ignoring the term ???? as it is very small)
?˜(?? -?? )
2
???
2
+?? 2
?? ?
2
+2(?? -?? )???
?? ?
Now potential energy,
Now lagrange,
?? =-???? (?? -?? )cos??? -?? '
?? {(?? -?? )cos??? -?? cos??? }
?? =?? -?? ?? =
1
2
?? '
{(?? -?? )
2
???
2
+?? 2
???
2
+2(?? -?? )?? ???
?? ?
}+
Take this point as zero potential
As
1
2
?? (?? -?? )
2
???
2
+
1
2
×
2
5
?? ?? 2
?? ?
2
+???? (?? -?? )cos??? +
?? '
?? {(?? -?? )cos??? -?? cos??? }
So, the generalised coordinate will only be one
Convert ?? to ?? .
Also
(?? -?? )???
=?? ?? ?
So,
?? =
1
2
?? '
{?? ?? ?
2
+?? 2
?? ?
2
+2?? 2
???
2
}+
1
2
?? ?? 2
?? ?
2
+
?? ?? 2
5
?? ?
2
+???? (?? -?? )cos??? ?+?? '
?? (?? -?? )cos??? -?? '
???? cos???
?? ?=?? ?
2
(2?? '
+
7?? 10
)?? 2
+(?? +?? '
)?? (?? -?? )cos?
????
?? -?? -?? '
???? cos??? ??? ??? ?
?=2?? ?
(2?? '
+
7?? 10
)?? 2
??? ??? ?
?=
?? (?? -?? )
(?? +?? '
)?? (?? -?? )(-1)sin?
????
(?? -?? )
+?? '
???? sin??? ?=-?? (?? +?? '
)?? sin?
????
(?? -?? )
+?? '
???? sin???
But
sin?
????
?? -?? ˜
????
?? -?? and sin??? ˜??
So,
??? ??? =-?? (?? +?? '
)?? ????
(?? -?? )
+?? '
??????
Now, using Lagrange's theorem
or
?? ????
(
??? ????
)-
??? ??? =0
?? ¨
(4?? '
+
7?? 5
)?? 2
+?? (?? +?? '
)
?????? ?? -?? -?? ?? '
????
?? ¨
(4?? '
+
7?? 5
)?? 2
+?????? [
?? (?? +?? '
)-?? '
(?? -?? )
?? -?? ]=0
?? ¨
+
?? ?? (4?? '
+
7?? 5
)?? 2
(
???(2?? -?? )+????
(?? -?? )
)?? =0
This is S.H.M. equation.
or
?? ¨
+???
2
?? =0
So,
?? 2
?=
?? {?? '
(2-
?? ?? )+?? }
(4?? '
+
7?? 5
)(?? -?? )
=
?? ?? ?? ?=
(4?? '
+
7?? 5
)(?? -?? )
?? +?? '
(2-
?? ?? )
Page 4
Edurev123
Mechanics and Fluid Dynamics
1. Generalised coordinate
1.1 A perfectly rough sphere of mass ?? and radius ?? , rests on the lowest point of
a fixed spherical cavity of radius ?? . To the highest point of the movable sphere is
attached a particle of mass ?? '
and the system is disturbed. Show that the
oscillations are the same as those of a simple pendulum of length
(?? -?? )
?? ?? '
+
?? ?? ?? ?? +?? '
(?? -
?? ?? )
(2009: 30 marks)
Solution:
Now,
?? ?? ''
?=?? ?? ''
???? ?=?? (?? +?? )
(?? -?? )?? ?=??
(?? -?? )???
?=?? ?? ?
Now, total kinetic energy, ?? can be written as
?? =
1
2
?? '
?? ?? 2
+
1
2
?? ?? ????
2
+
1
2
?? ????
?? 2
Now,
?? ?? ?=(?? -?? )sin??? ????
?? =(?? -?? )cos??? ·???
?? ?? ?=(?? -?? )cos??? ????
?? =(?? -?? )-sin??? ·???
?? ?? 2
?=???
?? 2
+???
?? 2
=(?? -?? )
2
???
2
?? ????
?=
2
5
?? ?? 2
and ?? =?? ?
?? ?? ?=(?? -?? )sin??? +?? sin??? ???
?? ?=(?? -?? )cos??? ·???
+?? cos??? ·?? ?
?? ?? ?=(?? -?? )cos??? -?? cos??? ???
?? ?=(?? -?? )(-sin??? )·???
+?? sin??? ·?? ?
???
?? 2
+???
?? 2
?=?? ?? 2
=(?? -?? )
2
???
2
+?? 2
?? ?
2
+2(?? -?? )???
?? ?
?? (cos??? cos??? -sin??? sin??? )
?=(?? -?? )
2
???
2
+?? 2
?? ?
2
+2(?? -?? )???
?? ?
(?? ·†
?
-???? )? (ignoring the term ???? as it is very small)
?˜(?? -?? )
2
???
2
+?? 2
?? ?
2
+2(?? -?? )???
?? ?
Now potential energy,
Now lagrange,
?? =-???? (?? -?? )cos??? -?? '
?? {(?? -?? )cos??? -?? cos??? }
?? =?? -?? ?? =
1
2
?? '
{(?? -?? )
2
???
2
+?? 2
???
2
+2(?? -?? )?? ???
?? ?
}+
Take this point as zero potential
As
1
2
?? (?? -?? )
2
???
2
+
1
2
×
2
5
?? ?? 2
?? ?
2
+???? (?? -?? )cos??? +
?? '
?? {(?? -?? )cos??? -?? cos??? }
So, the generalised coordinate will only be one
Convert ?? to ?? .
Also
(?? -?? )???
=?? ?? ?
So,
?? =
1
2
?? '
{?? ?? ?
2
+?? 2
?? ?
2
+2?? 2
???
2
}+
1
2
?? ?? 2
?? ?
2
+
?? ?? 2
5
?? ?
2
+???? (?? -?? )cos??? ?+?? '
?? (?? -?? )cos??? -?? '
???? cos???
?? ?=?? ?
2
(2?? '
+
7?? 10
)?? 2
+(?? +?? '
)?? (?? -?? )cos?
????
?? -?? -?? '
???? cos??? ??? ??? ?
?=2?? ?
(2?? '
+
7?? 10
)?? 2
??? ??? ?
?=
?? (?? -?? )
(?? +?? '
)?? (?? -?? )(-1)sin?
????
(?? -?? )
+?? '
???? sin??? ?=-?? (?? +?? '
)?? sin?
????
(?? -?? )
+?? '
???? sin???
But
sin?
????
?? -?? ˜
????
?? -?? and sin??? ˜??
So,
??? ??? =-?? (?? +?? '
)?? ????
(?? -?? )
+?? '
??????
Now, using Lagrange's theorem
or
?? ????
(
??? ????
)-
??? ??? =0
?? ¨
(4?? '
+
7?? 5
)?? 2
+?? (?? +?? '
)
?????? ?? -?? -?? ?? '
????
?? ¨
(4?? '
+
7?? 5
)?? 2
+?????? [
?? (?? +?? '
)-?? '
(?? -?? )
?? -?? ]=0
?? ¨
+
?? ?? (4?? '
+
7?? 5
)?? 2
(
???(2?? -?? )+????
(?? -?? )
)?? =0
This is S.H.M. equation.
or
?? ¨
+???
2
?? =0
So,
?? 2
?=
?? {?? '
(2-
?? ?? )+?? }
(4?? '
+
7?? 5
)(?? -?? )
=
?? ?? ?? ?=
(4?? '
+
7?? 5
)(?? -?? )
?? +?? '
(2-
?? ?? )
or,
So, oscillations are the same as those of a simple pendulum of above length
?? =
(4?? '
+
7?? 5
)(?? -?? )
?? +?? '
(2-
?? ?? )
1.2 A sphere of radius a and mass ?? rolls down a rough plane inclined at an angle
?? to the horizontal. If ?? be the distance of the point of contact of sphere from a
fixed point on the plane, find the acceleration by using Hamilton's equations.
(2010 : 30 Marks)
Solution:
Figure-1 below depicts the situation given in problem.
?? ? Radius of gyration of given sphere
Kinetic energy,
?? ?=
1
2
?? (???
2
+?? 2
???
2
)
?=
1
2
?? (???
2
+
2
5
?? 2
???
2
)
?=
1
2
?? (???
2
+
2
5
???
2
)=
7
10
?? ???
2
Figure-1
(?? =
2
?? ?? 2
for sphere )
(In pure rolling, ??? =?? ???
)
Potential energy,
?? =-?????? sin
Page 5
Edurev123
Mechanics and Fluid Dynamics
1. Generalised coordinate
1.1 A perfectly rough sphere of mass ?? and radius ?? , rests on the lowest point of
a fixed spherical cavity of radius ?? . To the highest point of the movable sphere is
attached a particle of mass ?? '
and the system is disturbed. Show that the
oscillations are the same as those of a simple pendulum of length
(?? -?? )
?? ?? '
+
?? ?? ?? ?? +?? '
(?? -
?? ?? )
(2009: 30 marks)
Solution:
Now,
?? ?? ''
?=?? ?? ''
???? ?=?? (?? +?? )
(?? -?? )?? ?=??
(?? -?? )???
?=?? ?? ?
Now, total kinetic energy, ?? can be written as
?? =
1
2
?? '
?? ?? 2
+
1
2
?? ?? ????
2
+
1
2
?? ????
?? 2
Now,
?? ?? ?=(?? -?? )sin??? ????
?? =(?? -?? )cos??? ·???
?? ?? ?=(?? -?? )cos??? ????
?? =(?? -?? )-sin??? ·???
?? ?? 2
?=???
?? 2
+???
?? 2
=(?? -?? )
2
???
2
?? ????
?=
2
5
?? ?? 2
and ?? =?? ?
?? ?? ?=(?? -?? )sin??? +?? sin??? ???
?? ?=(?? -?? )cos??? ·???
+?? cos??? ·?? ?
?? ?? ?=(?? -?? )cos??? -?? cos??? ???
?? ?=(?? -?? )(-sin??? )·???
+?? sin??? ·?? ?
???
?? 2
+???
?? 2
?=?? ?? 2
=(?? -?? )
2
???
2
+?? 2
?? ?
2
+2(?? -?? )???
?? ?
?? (cos??? cos??? -sin??? sin??? )
?=(?? -?? )
2
???
2
+?? 2
?? ?
2
+2(?? -?? )???
?? ?
(?? ·†
?
-???? )? (ignoring the term ???? as it is very small)
?˜(?? -?? )
2
???
2
+?? 2
?? ?
2
+2(?? -?? )???
?? ?
Now potential energy,
Now lagrange,
?? =-???? (?? -?? )cos??? -?? '
?? {(?? -?? )cos??? -?? cos??? }
?? =?? -?? ?? =
1
2
?? '
{(?? -?? )
2
???
2
+?? 2
???
2
+2(?? -?? )?? ???
?? ?
}+
Take this point as zero potential
As
1
2
?? (?? -?? )
2
???
2
+
1
2
×
2
5
?? ?? 2
?? ?
2
+???? (?? -?? )cos??? +
?? '
?? {(?? -?? )cos??? -?? cos??? }
So, the generalised coordinate will only be one
Convert ?? to ?? .
Also
(?? -?? )???
=?? ?? ?
So,
?? =
1
2
?? '
{?? ?? ?
2
+?? 2
?? ?
2
+2?? 2
???
2
}+
1
2
?? ?? 2
?? ?
2
+
?? ?? 2
5
?? ?
2
+???? (?? -?? )cos??? ?+?? '
?? (?? -?? )cos??? -?? '
???? cos???
?? ?=?? ?
2
(2?? '
+
7?? 10
)?? 2
+(?? +?? '
)?? (?? -?? )cos?
????
?? -?? -?? '
???? cos??? ??? ??? ?
?=2?? ?
(2?? '
+
7?? 10
)?? 2
??? ??? ?
?=
?? (?? -?? )
(?? +?? '
)?? (?? -?? )(-1)sin?
????
(?? -?? )
+?? '
???? sin??? ?=-?? (?? +?? '
)?? sin?
????
(?? -?? )
+?? '
???? sin???
But
sin?
????
?? -?? ˜
????
?? -?? and sin??? ˜??
So,
??? ??? =-?? (?? +?? '
)?? ????
(?? -?? )
+?? '
??????
Now, using Lagrange's theorem
or
?? ????
(
??? ????
)-
??? ??? =0
?? ¨
(4?? '
+
7?? 5
)?? 2
+?? (?? +?? '
)
?????? ?? -?? -?? ?? '
????
?? ¨
(4?? '
+
7?? 5
)?? 2
+?????? [
?? (?? +?? '
)-?? '
(?? -?? )
?? -?? ]=0
?? ¨
+
?? ?? (4?? '
+
7?? 5
)?? 2
(
???(2?? -?? )+????
(?? -?? )
)?? =0
This is S.H.M. equation.
or
?? ¨
+???
2
?? =0
So,
?? 2
?=
?? {?? '
(2-
?? ?? )+?? }
(4?? '
+
7?? 5
)(?? -?? )
=
?? ?? ?? ?=
(4?? '
+
7?? 5
)(?? -?? )
?? +?? '
(2-
?? ?? )
or,
So, oscillations are the same as those of a simple pendulum of above length
?? =
(4?? '
+
7?? 5
)(?? -?? )
?? +?? '
(2-
?? ?? )
1.2 A sphere of radius a and mass ?? rolls down a rough plane inclined at an angle
?? to the horizontal. If ?? be the distance of the point of contact of sphere from a
fixed point on the plane, find the acceleration by using Hamilton's equations.
(2010 : 30 Marks)
Solution:
Figure-1 below depicts the situation given in problem.
?? ? Radius of gyration of given sphere
Kinetic energy,
?? ?=
1
2
?? (???
2
+?? 2
???
2
)
?=
1
2
?? (???
2
+
2
5
?? 2
???
2
)
?=
1
2
?? (???
2
+
2
5
???
2
)=
7
10
?? ???
2
Figure-1
(?? =
2
?? ?? 2
for sphere )
(In pure rolling, ??? =?? ???
)
Potential energy,
?? =-?????? sin
? ?? =?? -?? =
7
10
?? ???
2
+???? ?? sin??? Now, ?? ?? =
??? ????
=
7
10
?? ×2???=
7
5
?? ???
? ??? =
5?? ?? 7?? ? Hamiltonian, ?? =-?? +?? ?? ·??? =-
7
10
?? ???
2
-?????? sin??? +?? ?? ·
5?? ?? 7?? ? ?? =
-5?? ?? 2
14?? -?????? sin??? +
5?? ?? 2
7?? ? ?? =
5
14?? ?? ?? 2
-???? ?? sin??? ( Putting ???=
5?? ?? 7?? )
? One of the Hamiltonian's equation gives
???
?? ?=
-??? ??? =+???? sin??? ??
7
5
?? ??¨?=???? sin??? ????¨?=
5
7
?? sin???
? Acceleration of sphere is
5
7
?? sin??? .
1.3 Obtain the equations governing the motion of a spherical pendulum.
(2012 : 12 Marks)
Solution:
Let ' ?? ' be the mass of the bob of spherical pendulum, which can swing in any direction,
traces out a sphere of constant length ?? .
Using polar co-ordinates ?? and ?? , the kinetic energy,
and potential energy,
?? ?=
1
2
?? (???
2
+?? 2
???
2
+?? 2
sin
2
??? ?? ?
2
)
?? ?=-?????? cos???
For spherical pendulum, the length ' ?? ' is constant.
Read More
|
387 videos|203 docs
|
Related Exams
About this Document
|
Nov 21, 2024 Last updated |
Document Description: Generalised coordinate for UPSC 2024 is part of Mathematics Optional Notes for UPSC preparation.
The notes and questions for Generalised coordinate have been prepared according to the UPSC exam syllabus. Information about Generalised coordinate covers topics
like and Generalised coordinate Example, for UPSC 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Generalised coordinate.
Introduction of Generalised coordinate in English is available as part of our Mathematics Optional Notes for UPSC
for UPSC & Generalised coordinate in Hindi for Mathematics Optional Notes for UPSC course.
Download more important topics related with notes, lectures and mock test series for UPSC
Exam by signing up for free. UPSC: Generalised coordinate | Mathematics Optional Notes for UPSC
Description
Full syllabus notes, lecture & questions for Generalised coordinate | Mathematics Optional Notes for UPSC - UPSC | Plus excerises question with solution to help you revise complete syllabus for Mathematics Optional Notes for UPSC | Best notes, free PDF download
Information about Generalised coordinate
In this doc you can find the meaning of Generalised coordinate defined & explained in the simplest way possible. Besides explaining types of
Generalised coordinate theory, EduRev gives you an ample number of questions to practice Generalised coordinate tests, examples and also practice UPSC
tests
|
Explore Courses for UPSC exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
Generalised coordinate | Mathematics Optional Notes for UPSC
,practice quizzes
,Sample Paper
,Extra Questions
,Exam
,Important questions
,Objective type Questions
,past year papers
,video lectures
,ppt
,Previous Year Questions with Solutions
,Generalised coordinate | Mathematics Optional Notes for UPSC
,Summary
,Viva Questions
,MCQs
,Generalised coordinate | Mathematics Optional Notes for UPSC
,shortcuts and tricks
,mock tests for examination
,study material
,Free
,Semester Notes
;
Additional Information about Generalised coordinate for UPSC Preparation
Generalised coordinate Free PDF Download
The Generalised coordinate is an invaluable resource that delves deep into the core of the UPSC exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the Generalised coordinate now and kickstart your journey towards success in the UPSC exam.
Importance of Generalised coordinate
The importance of Generalised coordinate cannot be overstated, especially for UPSC aspirants.
This document holds the key to success in the UPSC exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
Generalised coordinate Notes
Generalised coordinate Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to Generalised coordinate.
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, Generalised coordinate Notes on EduRev are your ultimate resource for success.
Generalised coordinate UPSC Questions
The "Generalised coordinate UPSC Questions" guide is a valuable resource for all aspiring students preparing for the
UPSC exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study Generalised coordinate on the App
Students of UPSC can study Generalised coordinate alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Generalised coordinate,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Generalised coordinate is prepared as per the latest UPSC syllabus.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily