An object weighs 0.25N in air and 0.01N when immersed in water. Calculate
(a) its relative density
(b) its apparent weight in a liquid of density 800kgm^-3
0.1kg
Relative density is equal to 0.25 : 0.01 = 0.25/0.01 = 25
a) R.d = 1.04
To calculate the relative density of the object, we need to find the ratio of the density of the object to the density of water. The density of water is approximately 1000 kg/m³.
(a) Relative density = (density of object) / (density of water)
First, let's calculate the density of the object:
Density of object = Weight of object in air / Acceleration due to gravity
Weight of object in air = 0.25 N
Acceleration due to gravity = 9.8 m/s² (approximately)
Density of object = 0.25 N / 9.8 m/s² = 0.0255 kg/m³
Now we can calculate the relative density:
Relative density = 0.0255 kg/m³ / 1000 kg/m³ = 0.0000255
(b) To find the apparent weight of the object in a liquid, we can use Archimedes' principle:
Apparent weight = Weight of object in air - Buoyant force
The buoyant force is the weight of the liquid displaced by the object, which can be calculated using the formula:
Buoyant force = Density of liquid x Volume of displaced liquid x Acceleration due to gravity
Density of the liquid is given as 800 kg/m³.
To calculate the volume of displaced liquid, we can divide the weight of the object in air by the density of the liquid.
Volume of displaced liquid = Weight of object in air / Density of liquid
Weight of object in air = 0.25 N
Density of liquid = 800 kg/m³
Volume of displaced liquid = 0.25 N / 800 kg/m³ = 0.0003125 m³
Now we can calculate the buoyant force:
Buoyant force = 800 kg/m³ x 0.0003125 m³ x 9.8 m/s² = 0.0245 N
Finally, we can find the apparent weight of the object:
Apparent weight = 0.25 N - 0.0245 N = 0.2255 N