Ask a Doubt
Request a call back

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

CBSE Class 12-science Answered

A metallic solid sphere is rotating about its diameter as axis of rotation . If the temperature is increased by 200∘C200∘C, the percentage increase in its moment of inertia is : (Coefficient of linear expansion of the metal =10−5/∘C=10−5/∘C)
Asked by Atulcaald | 31 May, 2018, 09:30: PM
answered-by-expert Expert Answer
Change in volume δV due to thermal expansion is given by
 
begin mathsize 12px style delta V space equals space V subscript 0 gamma capital delta T space................. left parenthesis 1 right parenthesis end style
where V0 is initial volume, γ is volume expansion coefficient and ΔT is increase of temperature.
 
change in volume as a function of change in radius is given by
 
begin mathsize 12px style delta V space equals space 4 over 3 pi open parentheses R plus delta R close parentheses cubed space minus 4 over 3 pi R cubed space equals space 4 over 3 pi R cubed open square brackets open parentheses 1 plus fraction numerator delta R over denominator R end fraction close parentheses cubed minus space 1 close square brackets space equals V subscript 0 open square brackets open parentheses 1 plus fraction numerator 3 delta R over denominator R end fraction close parentheses minus space 1 close square brackets space because delta R space less than less than space R h e n c e space space delta V space equals space V subscript 0 fraction numerator 3 delta R over denominator R end fraction............................ left parenthesis 2 right parenthesis end style
 
from (1) and (2), we get begin mathsize 12px style fraction numerator delta R over denominator R end fraction space equals space gamma over 3 capital delta T space equals space alpha capital delta T space space............................. left parenthesis 3 right parenthesis end style
where α is linear expansion coefficient ( γ = 3α )
 
Moment of inertia I is given by, I = K×R2 ....................(4)
where all constants are clubbed together as K.
 
change in moment of inertia δI due to change in radius δR is given by,
δI = 2×R×K×δR ...................(5)
 
from (4) and (5), we get begin mathsize 12px style fraction numerator delta I over denominator I end fraction space equals space fraction numerator 2 delta R over denominator R end fraction end style...................(6)
using eqn(3), we rewrite eqn(6) to get percentage change as,
begin mathsize 12px style fraction numerator delta I over denominator I end fraction cross times 100 space equals space 2 fraction numerator delta R over denominator R end fraction cross times 100 space equals space 2 cross times alpha cross times capital delta T cross times 100 space equals space 2 cross times 10 to the power of negative 5 end exponent cross times 200 cross times 100 space equals space 0.4 percent sign end style
Answered by Thiyagarajan K | 09 Jun, 2018, 11:09: 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
question image
Asked by r01raunak | 23 May, 2023, 10:24: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
Kirchhoff law
Asked by komalbrar0987 | 17 May, 2023, 06:15: PM
ANSWERED BY EXPERT 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 ANSWERED BY EXPERT
CBSE 12-science - Physics
semi conductor
Asked by Abhishek | 23 Mar, 2023, 08:37: PM
ANSWERED BY EXPERT 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 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 ANSWERED BY EXPERT
CBSE 12-science - Physics
Please answer below question from 2023 board paper:  
question image
Asked by prachis14 | 06 Mar, 2023, 04:49: PM
ANSWERED BY EXPERT 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 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 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 ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt