A metal ball of density 7800 kg/m^3 is suspected to have a large number of cavities . It weigh

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9-1.Fluid Mechanics

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A metal ball of density $7800\ kg/m^3$ is suspected to have a large number of cavities . It weighs $9.8$ $kg$ when weighed directly on a balance and $1.5$ $kg$ less when immersed in water . The fraction by volume of the cavities in the metal ball is approximately ....... $\%$

A

$20$

B

$30$

C

$16 $

D

$11$

Solution

$9.8=7800\left(\mathrm{v}_{\mathrm{s}}\right){\mathrm{g}}$

$1.5=1000\left(\mathrm{v}_{\mathrm{s}}+\mathrm{v}_{\mathrm{e}}\right) \mathrm{g}$

$\frac{v_{s}}{v_{s}+v_{c}}=\frac{9.8}{1.5} \times \frac{10}{78}=83.76 \%$

$\frac{\mathrm{v}_{\mathrm{e}}}{\mathrm{v}_{\mathrm{s}}+\mathrm{v}_{\mathrm{c}}} \simeq 16 \%$

Standard 11

Physics

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