# A metal cube of edge 5 cm and density 9.0 g/cm^3 is suspended by a thread so as to completely immersed in a liquid of density 1.2g/cm^3. Find the tension in thread. g = 10m/s^2

Side of the cube, a = 5 cm

Volume of metal cube, V = a3 = (5 cm)×3 = 125 cm3 = 125 x 10−6 m3

Density of metal, d = 9 g/cm3 = 9000 kg/m3.
Mass of the metal cube m = volume x density
= 125 x 10−6 m3×9000 kg/m3
= 1.125 kg
Weight of the metal cube in air, W = mg = 1.125 kg x 10 m/s2 = 11.25 N
The cube immersed in a liquid of density = 1.2 g/cm3 = 1200 kg/m3
Volume of liquid displaced = Volume of metal cube = 125 x 10−6 m3

Mass of liquid displaced = Volume x density of liquid

= 125 x 10−6 m3×1200 kg/m3
=  0.15 kg
Weight of liquid displaced = 0.15  kg x 10 m/s2 = 1.5 N = upthrust

Weight of metal cube in liquid = Weight of the metal cube in air - upthrust
= 11.25 − 1.5
=  9.75 N
Therefore tension in the string = 9.75 N

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Mass of the metal cube m = volume x density   = 125 x 10^−6 m^3 x 9000 kg/m^3. = 1.125 kg

Weight of the metal cube in air = mg = 1.125 kg x 10 ms^-2 = 11.25 N

Volume of liquid displaced = Volume of metal cube = 125 x 10^−6 m^3.

Mass of liquid displaced = Volume x density of liquid

= 125 x 10^−6 m^3.1200 kg/m^3.

=  0.15 kg

Weight of liquid displaced = 0.15  kg x 10 m/s^2 = 1.5 N = upthrust

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