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
Asked by mufeedatvp2000 | 18 Apr, 2020, 02:22: PM
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 Subjective Questions Webinar Subjective Questions Pre Board Assessment
Answered Unanswered My Questions My Answers
CBSE 12-science - Physics
answer
Asked by r01raunak | 23 May, 2023, 10:24: AM
ANSWERED BY EXPERT
CBSE 12-science - Physics
Kirchhoff law
Asked by komalbrar0987 | 17 May, 2023, 06:15: PM
ANSWERED BY EXPERT
CBSE 12-science - Physics
obtain the lens formula in case of concave lens
Asked by marvellouskyndiah | 17 May, 2023, 08:07: AM
ANSWERED BY EXPERT
CBSE 12-science - Physics
semi conductor
Asked by Abhishek | 23 Mar, 2023, 08:37: PM
ANSWERED BY EXPERT
CBSE 12-science - Physics
Soft iron is used to make the core of transformer because of it's.....  a) low coercivity and low retentivity b) high corecivity and low retentivity Chose correct option and give reason. 
Asked by Jayashri | 06 Mar, 2023, 06:47: PM
ANSWERED BY EXPERT
CBSE 12-science - Physics
Please answer this question. Draw a graph showing the variation of binding energy per nucleon as a function of mass number A. The binding energy per nucleon for heavy nuclei (A > 170) decreases with the increase in mass number. Explain.
Asked by varma.renu9481 | 06 Mar, 2023, 05:44: PM
ANSWERED BY EXPERT
CBSE 12-science - Physics
Please answer below question from 2023 board paper:  
Asked by prachis14 | 06 Mar, 2023, 04:49: PM
ANSWERED BY EXPERT
CBSE 12-science - Physics
An inductor, a capacitor and a resistor are connected in series across an ac source of voltage. If the frequency of the source is decreased gradually. the reactance of: (a) both the inductor and the capacitor decreases. (b) inductor decreases and the capacitor increases. (c) both the inductor and the capacitor increases. (d) inductor increases and the capacitor decreases.
Asked by paresh0311 | 06 Mar, 2023, 04:42: PM
ANSWERED BY EXPERT
CBSE 12-science - Physics
Answer this:  Assertion (A): When radius of a circular loop carrying a steady current is doubled, its magnetic moment becomes four times.  Reason (R): The magnetic moment of a circular loop carrying a steady current is proportional to the area of the loop.  Select the correct answer from the codes (a), (b), (c) and (d) as given belote.  (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).  (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).  (c) Assertion (A) is true, but Reason (R) is false.  (d) Assertion (A) is false and Reason (R) is also false.
Asked by anubhutiupadhaya | 06 Mar, 2023, 04:23: PM
ANSWERED BY EXPERT
CBSE 12-science - Physics
Please answer this.  What is meant by the term 'displacement current'? Briefly explain how this current is different from a conduction current.
Asked by sagarmishra | 06 Mar, 2023, 04:07: PM
ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt