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  • Please,please help me The relative error in the determination of the surface area of a sphere is α. Then the relative error in the determination of its volume is :-2

The relative error in the determination of the surface area of a sphere is α. Then the relative error in the determination of its volume is :

  • Option 1)

    \frac{3}{2}\alpha

     

     

     

  • Option 2)

    \frac{2}{3}\alpha

  • Option 3)

    \frac{5}{2}\alpha

  • Option 4)

    \alpha

 

Answers (2)

best_answer

As we have learned

Error in quantity raised to some power -

x=\frac{a^{n}}{b^{m}}\rightarrow \frac{\Delta x}{x}=\pm \left ( n\frac{\Delta a}{a}+m\frac{\Delta b}{b} \right )

- wherein

\Delta a= absolute error in measurement of a

\Delta b= absolute error in measurement of b

\Delta x= absolute error in measurement of x

 

 For a sphere , v = \frac{4 \pi }{3} r^3

\Rightarrow \frac{\Delta v}{v}= 3 \cdot \frac{\Delta r}{r}........(1)

Surface area A = 4 \pi r^2

  \Rightarrow \frac{\Delta A}{A}= 2 \cdot \frac{\Delta r}{r}........(2)

\frac{\Delta v/v}{\Lambda A/A } = 3/2 \Rightarrow \frac{\Delta v}{v}= 3 \alpha /2

 

 

 

 


Option 1)

\frac{3}{2}\alpha

 

 

 

Option 2)

\frac{2}{3}\alpha

Option 3)

\frac{5}{2}\alpha

Option 4)

\alpha

Posted by

SudhirSol

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JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

option 1

 

Posted by

Kalyani Mahant

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