Question

A solid of mass 1.3kg, suspended by a string is completely in water. If the tension in the string is 6.0N, calculate;

i) the upthrust on the solid
ii) volume of the solid
iii) its density
(g=10m/s^2 , density of water=1000kg/m^3)​

Answer 1

1:- The upthrust on the solid:- 0.013N

2:- Volume of the solid:- 1.3 Kg/density

3) Density:- 46.15 Kg/m^3

Step-by-step explanation:

1) The upthrust on the solid is equal to the weight of the water displaced by the solid, which is given by Archimedes' principle. Therefore, we can calculate the upthrust using the formula:

Upthrust = Weight of water displaced = Volume of water displaced x Density of water x Gravity

Since the solid is completely submerged in water, the volume of water displaced is equal to the volume of the solid.

Thus:

Upthrust = Volume of solid x Density of water x Gravity

Upthrust = (1.3 kg / 1000 kg/m^3) x 10 m/s^2

Upthrust = 0.013 N

2) We can use the formula for density to calculate the volume of the solid, which is given by:

Density = Mass / Volume

Rearranging the formula:

Volume = Mass / Density

Volume = 1.3 kg / Density

We know from part (i)

that the upthrust on the solid is equal to the weight of the water displaced, which means that the solid is in equilibrium (i.e., the forces acting on it are balanced).

Therefore:

Weight of the solid = Tension in the string

Weight of the solid = Mass x Gravity

Mass = Weight of the solid / Gravity

Mass = 6.0 N / 10 m/s^2

Mass = 0.6 kg

Substituting the values for mass and density, we get:

Volume = 0.6 kg / Density

0.013 m^3 = 0.6 kg / Density

Density = 0.6 kg / 0.013 m^3

Density = 46.15 kg/m^3.