# 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

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,

$x=1050$

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