Ask a Doubt
Request a call back

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

CBSE Class 12-science Answered

pls explain
question image
Asked by mufeedatvp2000 | 18 Apr, 2020, 14:22: PM
answered-by-expert Expert Answer
Let us find the centre of mass of semi circular ring of radius R .
From the given figure above, if we consider origin of X-Y coordinate system is at center of semi-circular ring,
then centre of mass is in y-axis by symmetry, i.e. x-coordinate Cx of centre of mass is zero.
 
y-coordinate Cy of centre of mass is given by
 
begin mathsize 14px style C subscript y space equals space 1 over M integral d m space y space equals space 1 over M integral subscript 0 superscript theta rho space R d theta space R sin theta space equals fraction numerator rho space R squared over denominator M end fraction space integral subscript 0 superscript theta sin theta space d theta space equals space fraction numerator 2 space rho space R squared over denominator M end fraction end style  ........................(1)
where M is mass of semi-circular ring, dm is mass of a small element of length dl .
 
Let radial line connecting the element dl makes angle θ with x-axis and dθ be angle subtended  by element dl at centre.
 
ρ is mass per unit length of wire.  Mass M of wire is obtained as M = ρ ( π R )
 
Using the substitution  ( ρ/M ) = 1/( π R ) ,  equation (1) for y-coordinate of centre of mass becomes
 
Cy = 2R/π
 
Moment of inertia I about centre of mass is given by
 
begin mathsize 14px style I space equals space integral d m space r squared space equals space integral subscript 0 superscript pi R space d theta space rho space open curly brackets R squared cos squared theta space plus space open parentheses R space sin theta space minus space fraction numerator 2 R over denominator pi end fraction close parentheses squared close curly brackets end style
we get from above integration, begin mathsize 14px style I space equals space M space open curly brackets 1 space minus space 4 over pi squared close curly brackets R squared end style
Answered by Thiyagarajan K | 19 Apr, 2020, 07:54: AM

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 12-science - Physics
why current is scalar
Asked by jothisugashini216 | 16 Jul, 2024, 20:30: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
Half life Sums
Asked by prithviraj.chopra2011 | 14 Jul, 2024, 23:00: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
what is photp electric effect
Asked by basithhhabduuu | 14 Jul, 2024, 17:07: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
a small object place 10cm in front of a plane mirror If you stand behind the object 30cm from the mirror and look at it image the distance focused for your eye will be
Asked by asmaabid356 | 10 Jul, 2024, 21:03: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
an object 2cm high is placed at a distance of 16cm from a concave mirror which produces a virtual image 3cm high what is the focal length of the mirror ?
Asked by pushpamagadum21 | 09 Jul, 2024, 20:43: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
01. A thin ring of radius R metre has charge q coulomb uniformly spread on it. The ring rotates about its axis with a constant frequency f revolution/s. The value of magnetic field in tesla at the centre of the ring is
Asked by sumitghorband09 | 20 Jun, 2024, 21:42: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
please solve this
question image
Asked by axonuploadserver4 | 14 Jun, 2024, 17:41: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
question image
Asked by goswamideepak16492 | 12 Jun, 2024, 10:18: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
A ball is thrown up with certain velocity so that it reaches a height h . Find the ratio of the times in which it is at h/3 .
Asked by trishaktiprasadmallik693 | 11 Jun, 2024, 07:17: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
there is no deviation
question image
Asked by rahuldevgayen4 | 10 Jun, 2024, 14:58: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Are You a Teacher or a Parent Seeking Customised Tests? Click here
×