Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 11-science Answered

What is the centre of mass of parabolic area

Asked by rushabhjain.avv | 23 Oct, 2019, 07:18: PM
Expert Answer
Figure shows a lamina of parabolic shape of length L from apex.
 
Let the parobolic curve equation be y2 = k x and apex coincides with origin
 
Let us consider a thin strip of width dx at a distance x from origin.
 
Area of this strip = 2 (kx)1/2 dx ;
If ρ is uniform density ( mass per unit area) of plate then its mass = 2 ρ(kx)1/2 dx
 
By symmetry y-coordinate of centre mass is on x-axis i.e. y = 0 ;
 
x-coordinate cx of Centre of mass of given lamina of parabolic shape  is given by

begin mathsize 12px style c x space equals space 1 over M integral subscript 0 superscript L x space 2 square root of k x end root space space rho space d x end style.........................(1)
Mass of whole lamina is given by

begin mathsize 12px style M space equals space integral subscript 0 superscript L 2 space square root of k space x end root space rho space d x end style ...........................(2)
Hence x-coordinate cx of Centre of mass of given lamina of parabolic shape  is given by
 
begin mathsize 12px style c x space equals space fraction numerator integral subscript 0 superscript L x space 2 square root of k x end root space space rho space d x over denominator integral subscript 0 superscript L space 2 square root of k x end root space space rho space d x end fraction space equals space 3 over 5 L end style
Answered by Thiyagarajan K | 23 Oct, 2019, 08:58: PM
Multiple Choice Questions Practice Test Subjective Questions Webinar Subjective Questions Pre Board Assessment
Answered Unanswered My Questions My Answers
CBSE 11-science - Physics
why the value of g is zero at the centre of the earth
Asked by ubarhandepramod | 21 Nov, 2022, 03:49: PM
ANSWERED BY EXPERT
CBSE 11-science - Physics
1. EXPLAIN HOW TO MEASURE DISTANCES USING THE PARALLAX METHOD (BCZ IT IS CONFUSING). 2. HOW DID THE MOLECULAR DISTANCE HAS BEEN FOUND USING THAT ACID(WHOLE PROCEDURE)?
Asked by muhammadkp356 | 16 Oct, 2022, 09:18: PM
ANSWERED BY EXPERT
CBSE 11-science - Physics
Que: Equal and opposite charges cancel out eachother's effect then why doesn't centrifugal force cancel out centripetal force's effect on a particle moving in circular motion?
Asked by advssdrall | 07 Oct, 2022, 11:11: PM
ANSWERED BY EXPERT
CBSE 11-science - Physics
Please give answer
Asked by ankurgoyal616 | 27 Sep, 2022, 03:07: PM
ANSWERED BY EXPERT
CBSE 11-science - Physics
A person goes to his office from his home daily at a fixed speed but today he decided to reduce his speed by 20% as a result he reaches his office 16 minute late. what's the actual time he takes to reach his office daily
Asked by prashantgaikwadfox000 | 25 Sep, 2022, 05:38: PM
ANSWERED BY EXPERT
CBSE 11-science - Physics
If I throw a projectile with velocity 8m/s then will the effect of air on it increase or decrease the velocity?
Asked by mahekacharya87 | 20 Sep, 2022, 10:41: AM
ANSWERED BY EXPERT
CBSE 11-science - Physics
one meter long string can bear maximum of 0.5 kg mass . a mass of 0.05 kg is tied to one end and rotated in a horizontal circle , calculate the maximum number of revolution so that string does not brakes
Asked by pushpakumari291279 | 20 Aug, 2022, 08:15: AM
ANSWERED BY EXPERT
CBSE 11-science - Physics
What do your understatnd by (1)position vector and (ii) displancment vector. Distinguish them with illustration.
Asked by rk274268 | 05 Aug, 2022, 01:19: PM
ANSWERED BY EXPERT
CBSE 11-science - Physics
what is the derivation of formula of gravity  
Asked by halderishan008 | 30 Jul, 2022, 07:28: PM
ANSWERED BY EXPERT
CBSE 11-science - Physics
what is dot product
Asked by Kattaithihaas | 24 Jul, 2022, 01:23: PM
ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Season Break Offer!
Get 60% Flat off instantly.
Avail Now
×