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Confusion in solution Q;A solid sphere of radius R of a material of bulk modulus B is surrounded by a liquid in a cylindrical container. A massless piston of area A floats on the surface of the liquid .Find the fractional change in the radius of the sphere (dR/R) when a mass M is placed on the piston to compress the liquid? on solving we take BULK MODULUS=Mg/A/delta V/V.....as we take V=4/3pieRcube but why we take delta V=4pieRsquare-deltaR instead of 4/3piedelRcube..........
Confusion in solution
Q;A solid sphere of radius R of a material of bulk modulus B is surrounded by a liquid in a cylindrical container. A massless piston of area A floats on the surface of the liquid .Find the fractional change in the radius of the sphere (dR/R) when a mass M is placed on the piston to compress the liquid?
on solving we take BULK MODULUS=Mg/A/delta V/V.....as we take V=4/3pieRcube but why we take delta V=4pieRsquare-deltaR instead of 4/3piedelRcube..........
from elementary differential calculus, d(R3)/dR =3R2, thus d(R3)=3R2dR,therefore deltaV=delta((4pi/3)R3)=(4pi/3)3R2dR 4piR2dR
from elementary differential calculus, d(R3)/dR =3R2, thus d(R3)=3R2dR,therefore deltaV=delta((4pi/3)R3)=(4pi/3)3R2dR
4piR2dR
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