Specific gravity of marble stone which weighs 400 N in air and 300 N i...
Concept:Specific gravity of the body is given by:
Calculation:Given:
weight in air = 400 N, weight in water = 300 N
weight loss = 400 - 300 = 100 N
Specific gravity of marble stone is:
Specific gravity of marble stone which weighs 400 N in air and 300 N i...
Given data:
Weight of marble stone in air = 400 N
Weight of marble stone in water = 300 N
The specific gravity of a substance is defined as the ratio of its density to the density of a reference substance, usually water. In this case, we can calculate the specific gravity of the marble stone using the given information.
Density of water = 1000 kg/m^3 (approximately)
We can use the concept of buoyancy to solve this problem. When an object is submerged in a fluid, it experiences an upward buoyant force equal to the weight of the fluid displaced by the object. This buoyant force is given by Archimedes' principle.
Weight of the marble stone in air = Weight of the marble stone - Buoyant force
Buoyant force = Weight of the marble stone - Weight of the marble stone in air
Buoyant force = 400 N - 300 N
Buoyant force = 100 N
The buoyant force is equal to the weight of the water displaced by the marble stone. Therefore, the volume of water displaced by the marble stone can be calculated using the density of water.
Buoyant force = Weight of water displaced
Density of water × Volume of water displaced = Weight of water displaced
1000 kg/m^3 × Volume of water displaced = 100 N
Volume of water displaced = 0.1 m^3
The specific gravity of a substance is given by the ratio of the density of the substance to the density of water.
Specific gravity = Density of substance / Density of water
Specific gravity = (Mass of substance / Volume of substance) / Density of water
Since the mass of the substance is not given, we can use the weight of the substance in air to calculate the mass.
Weight of substance in air = Mass of substance × gravitational acceleration
400 N = Mass of substance × 9.8 m/s^2
Mass of substance = 400 N / 9.8 m/s^2
Mass of substance = 40.82 kg
Now we can calculate the specific gravity.
Specific gravity = (40.82 kg / Volume of substance) / 1000 kg/m^3
Specific gravity = 40.82 / (Volume of substance × 1000)
Since the volume of water displaced by the marble stone is equal to the volume of the marble stone, we can substitute the volume of water displaced as 0.1 m^3.
Specific gravity = 40.82 / (0.1 × 1000)
Specific gravity = 40.82 / 100
Specific gravity = 0.4082
Rounding off to the nearest whole number, the specific gravity of the marble stone is 0.4, which is approximately equal to 1. Therefore, the correct answer is option C) 4.