A vessel contains oil of density 0.8gm//cm^(3) over mercury of density 13.6gm//cm^(3) .Solid sphere floats with half of its volume immersed in mercury and the other half in the oil . The density of the sphere is ….. gm//cm^(3).

A vessel contains oil of density 0.8gm//cm^(3) over mercury of density

1.	A vessel contains oil of density 0.8gm//cm^(3) over mercury of density 13.6gm//cm^(3) .Solid sphere floats with half of its volume immersed in mercury and the other half in the oil . The density of the sphere is ….. gm//cm^(3).
Answer» `3.3` `6.4` `7.2` `12.8` Solution : LET density of sphere is `rho` , Density of oil is `rho_(1)` and density of mercury is `rho_(2)` Weight of sphere `W=(4)/(3)PIR^(3)rhog`….(1) Where R= RADIUS of sphere BUOYANT force on sphere in oil , `F_(1)=(2)/(3)piR^(3)rho_(1)g`....(2) Buoyant force on sphere in mercury, `F_(2)=(2)/(3)piR^(2)rho_(2)g`....(3) Weight of sphere `W=F_(1)+F_(2)` `therefore(4)/(3)piR^(3)rhog=(2)/(3)piR^(3)rho_(1)g+(2)/(3)piR^(3)rho_(2)g` `therefore2rho=rho_(1)+rho_(2)` `therefore2rho=0.8+13.6` `therefore2rho=14.4` `thereforerho=7.2gcm^(-3)`