A spinal spring,loaded with a piece of metal,extends by 10.5cm in air.When the metal is fully submerged in water,the spring extends by 6.8cm.Calculate the relative density of the metal using Hooke's law

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To calculate the relative density of the metal using Hooke's law, we need to determine the change in weight of the metal when submerged in water.

Hooke's law states that the elongation or extension of a spring is directly proportional to the force applied. The equation to calculate this is:

F = kx

where:
F = force applied to the spring (weight of the metal)
k = spring constant
x = elongation or extension of the spring

In this case, we have two scenarios: the spring extending by 10.5 cm in air, and by 6.8 cm when the metal is submerged in water.

Using the given information, we can set up two equations:

1. 10.5 cm = kx1
2. 6.8 cm = kx2

We can divide these equations to eliminate the spring constant:

10.5 cm / 6.8 cm = (kx1)/(kx2)

Simplifying further, we get:

10.5 cm / 6.8 cm = x1 / x2

Now we can rearrange the equation to solve for the unknown, which is the relative density (ρ) of the metal:

ρ = (x1 / x2) * ρw

where:
ρw = density of water (assumed to be 1 g/cm^3)

In this case, we assume the density of water to be 1 g/cm^3. However, if the density of water is given, you can substitute the appropriate value.

Applying the values, we can calculate the relative density of the metal.

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