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  • The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is  <img alt="\left ( \frac{x}{100} \right )^{o}/_{o}" src="http://entrancecorner.codecogs.com/gif.latex?

The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is  \left ( \frac{x}{100} \right )^{o}/_{o} . If the relative errors in measuring the mass and diameter are 6% and 1.5 % respectively. The value of 'x' is  .............
Option: 1 1050
Option: 2 525
Option: 3 2100
Option: 4 4200

Answers (1)

best_answer

As we know-

\rho=\frac{m a s s}{V o l u m e}=\frac{m}{\frac{4}{3} \pi R^{3}}=\frac{m}{\frac{\pi}{6} D^{3}}

\Rightarrow \frac{\Delta \rho}{\rho }=\frac{\Delta m}{m}+3 \frac{\Delta D}{D}

\Rightarrow \frac{\Delta \rho}{\rho}=6+1.5 \times 3

\Rightarrow \left(\frac{x}{100}\right) \%=10.5 \cdot \%

So,

x=1050

 

 

 

Posted by

Deependra Verma

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