A solid weighs 0.040N in air and 0.024N when fully immersed in a liquid density 800kg. Calculate the volume of the solid (g=10mls)?
bouyant force= .04-.024=.016N
but that has to equal to the weight of the displaced liquid
.016=800kg/m^3l*g*volumedisplaced
volume displaced=.016/8000 m^3=2ml
To calculate the volume of the solid, we need to use the principle of buoyancy, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
Given:
Weight of the solid in air = 0.040 N
Weight of the solid in liquid = 0.024 N
Density of the liquid = 800 kg/m^3
Acceleration due to gravity (g) = 10 m/s^2
Let's break down the steps to find the volume:
1. Calculate the net force acting on the solid when it is submerged in the liquid:
Net Force = Weight in air - Weight in liquid
= 0.040 N - 0.024 N
= 0.016 N
2. Calculate the buoyant force acting on the solid:
Buoyant Force = Weight in air - Net Force
= 0.040 N - 0.016 N
= 0.024 N
3. Calculate the weight of the fluid displaced:
Weight of displaced fluid = Buoyant Force
= 0.024 N
4. Calculate the mass of the fluid displaced:
Mass of displaced fluid = Weight of displaced fluid / g
= 0.024 N / 10 m/s^2
= 0.0024 kg
5. Calculate the volume of the solid using the density of the liquid:
Volume = Mass of displaced fluid / Density of the liquid
= 0.0024 kg / 800 kg/m^3
= 0.000003 m^3
(Note: 1 m^3 = 1000 liters)
Therefore, the volume of the solid is 0.000003 m^3 or 0.003 liters.