Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Home

Class 11

Physics

System of Particles and Rotational Motion

Centre of mass

Figure shows a circular disc of radius R from which a small di

Question

Hard

Solving time: 4 mins

Figure shows a circular disc of radius $R$ from which a small disc is cut such that the periphery of the small disc touch the large disc and whose radius is $R /2$ . Find the centre of mass of the remaining part of the disc.

Name: Video solution 1: Figure shows a circular disc of radius R from which a small disc is cut such that the periphery of the small disc touch the large disc and whose radius is R/2. Find the centre of mass of the remaining part of the disc.
Uploaded: 2022-05-08T14:24:52.000Z
Duration: 10 min
Description: Video solution 1: Figure shows a circular disc of radius R from which a small disc is cut such that the periphery of the small disc touch the large disc and whose radius is R/2. Find the centre of mass of the remaining part of the disc.

Views: 5,714 students

Updated on: May 8, 2022

Book:

Physics Galaxy Mechanics Vol 1 (Ashish Arora)

Found 7 tutors discussing this question

Charlotte Discussed

Figure shows a circular disc of radius

R

from which a small disc is cut such that the periphery of the small disc touch the large disc and whose radius is

R /2

. Find the centre of mass of the remaining part of the disc.

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

Solution
If the disc shown in the figure were complete, its centre of mass lie at its geometric centre and the centre of mass of the smaller disc, which is removed, also lie at its centre. If from the bigger disc, the smaller one is removed then the centre of mass of the remaining portion will be somewhere on the left of the centre of the bigger disc. Let it be at a distance

x

from the centre. The analysis is shown in the figure. Now the centre of mass of the remaining portion and the removed disc must be at C.
Solution Image

If masses of the removed disc and the remaining portion are

m_{1}

and

m_{2}

, we have

m_{1} = \frac{M}{π R ^{2}} \times π \frac{R ^{2}}{4} = \frac{M}{4} m_{2} = M - \frac{M}{4} = \frac{3 M}{4}

Now applying the concept of centre of mass of a two body system we get the distance

x

at which the centre of mass of the remaining portion of the disc lie, as

x M x 4 x x = \frac{m _{1} ( x + R /2 )}{m _{1} + m _{2}} = \frac{M}{4} (x + \frac{R}{2}) = x + \frac{R}{2} = \frac{R}{6}

Was this solution helpful?

134

Report

Filo tutor solutions (1)

Learn from their 1-to-1 discussion with Filo tutors.

10 mins

Uploaded on: 5/8/2022

Ask your question, on a video call with tutor

Connect instantly with this tutor

Connect now

Taught by

Neelansh Agrawal

Total classes on Filo by this tutor - 742

Teaches : Physics, Organic Chemistry, Inorganic Chemistry

Connect instantly with this tutor

Connect now

Notes from this class (3 pages)

Download

Was this solution helpful?

Report

One destination for complete JEE/NEET preparation

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our Physics tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	Figure shows a circular disc of radius $R$ from which a small disc is cut such that the periphery of the small disc touch the large disc and whose radius is $R /2$ . Find the centre of mass of the remaining part of the disc.
Updated On	May 8, 2022
Topic	System of Particles and Rotational Motion
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 1
Upvotes	202
Avg. Video Duration	10 min

Figure shows a circular disc of radius $R$ from which a small disc is cut such that the periphery of the small disc touch the large disc and whose radius is $R /2$ . Find the centre of mass of the remaining part of the disc.

Text solutionVerified

Filo tutor solutions (1)

Practice questions from Physics Galaxy Mechanics Vol 1 (Ashish Arora)

Practice more questions from System of Particles and Rotational Motion

Practice questions on similar concepts asked by Filo students

Figure shows a circular disc of radius R from which a small disc is cut such that the periphery of the small disc touch the large disc and whose radius is R/2. Find the centre of mass of the remaining part of the disc.

Text solutionVerified

Filo tutor solutions (1)

Practice questions from Physics Galaxy Mechanics Vol 1 (Ashish Arora)

Practice more questions from System of Particles and Rotational Motion

Practice questions on similar concepts asked by Filo students

Related books for questions on System of Particles and Rotational Motion

Figure shows a circular disc of radius $R$ from which a small disc is cut such that the periphery of the small disc touch the large disc and whose radius is $R /2$ . Find the centre of mass of the remaining part of the disc.