Question

A metal cube of side 5 cm and density 7.9 g cm–3 is suspended by a thread and is immersed completely in a liquid of density 1.1 g cm–3. Find : (a) the weight of cube, (b) the upthrust on cube and (c) the tension in thread.

Answer 1

Weight of cube in air = 9.875 N

Upthrust = 1.375 N

Tension in the string = 8.5 N

Explanation:

Volume of metal cube = a^3 = 5*5*5 cm3 = 125 x 10−6 m3

Density of metal = 7.9 g/cm3 = 7900 kg/m3

Mass of the metal cube m = volume x density

= 125 x 10−6 * 7900 kg/m3.

 = 0.9875 kg

Weight of the metal cube in air = m*g = 0.9875 kg x 10 m/s2 = 9.875 N

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 * 1100

 =  0.1375 kg

Weight of liquid displaced = 0.1375  kg x 10 m/s2 = 1.375 N = upthrust

Weight of metal cube in liquid = Weight of the metal cube in air - upthrust

 = 9.875 − 1.375  

 =  8.5 N

Tension in the string = 8.5 N

Answer 2

Weight of cube in air = 9.875 N

Upthrust = 1.375 N

Tension in the string = 8.5 N

Explanation:

Volume of metal cube = a^3 = 5*5*5 cm3 = 125 x 10−6 m3

Density of metal = 7.9 g/cm3 = 7900 kg/m3

Mass of the metal cube m = volume x density

= 125 x 10−6 * 7900 kg/m3.

= 0.9875 kg

Weight of the metal cube in air = m*g = 0.9875 kg x 10 m/s2 = 9.875 N

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 * 1100

=  0.1375 kg

Weight of liquid displaced = 0.1375  kg x 10 m/s2 = 1.375 N = upthrust

Weight of metal cube in liquid = Weight of the metal cube in air - upthrust

= 9.875 − 1.375  

=  8.5 N

Tension in the string = 8.5 N