a coil of wire of cross section 0.75mm2 weighs 125g in air and 115g in water. the length of coil in cm is

To find the length of the coil in centimeters, we need to use Archimedes' principle, which states that the buoyant force experienced by an object submerged in a fluid is equal to the weight of the fluid displaced by the object. We know the weight of the coil in air and the weight of the coil in water, so we can calculate the volume of the coil.

First, let's calculate the volume of the coil in cubic centimeters (cm³).

1. Calculate the weight of the coil in air relative to its weight in water:
Weight in air = 125 g
Weight in water = 115 g
Weight difference = Weight in air - Weight in water = 125 g - 115 g = 10 g

2. Convert the weight difference to Newtons (1 N = 1000 g):
Weight difference in Newtons = 10 g * (1 N / 1000 g) = 0.01 N

3. Use the weight difference to calculate the volume of the coil in cubic centimeters:
Buoyant force = Weight difference
Buoyant force = Weight of the fluid displaced
Buoyant force = Density of water * Volume of coil * Acceleration due to gravity
Density of water = 1000 kg/m³ (or 1000 g/cm³)
Acceleration due to gravity = 9.8 m/s² (or 9.8 cm/s²)
Volume of coil = Buoyant force / (Density of water * Acceleration due to gravity)
Volume of coil = 0.01 N / (1000 g/cm³ * 9.8 cm/s²) = 0.00000102 m³ = 1.02 cm³

Now that we have the volume of the coil, we can calculate its length.

4. We know the cross-sectional area of the coil is 0.75 mm². In order to find the length, we can divide the volume by the cross-sectional area:
Volume of coil = Area of cross-section * Length of coil
Length of coil = Volume of coil / Area of cross-section
Length of coil = 1.02 cm³ / 0.75 mm²

5. Convert the cross-sectional area to square centimeters:
Area of cross-section = 0.75 mm² * (1 cm² / 100 mm²) = 0.0075 cm²

6. Substitute the values into the formula:
Length of coil = 1.02 cm³ / 0.0075 cm²

Calculating the length of the coil by dividing the volume by the cross-sectional area will give us the length in centimeters.