The specific gravity of a substance is given by G = DS/DW, where DS is the density of the substance in kg/m3 and DW is the density of water, which is known to be 1000 kg/m3. The density of a particular substance is measured to be DS = 500±5 kg/m3. Estimate the specific gravity, and find the uncertainty in the estimate

Explanation:

The specific gravity is given by,

Now, in order to calculate the uncertainty (relative error) in G, we must first take log (base e) on both sides of the equation,

Differentiating the above equation,

The second term is zero because it is known that and hence a constant.

Putting the appropriate values, we get,

Therefore, uncertainty in G =

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