An old coin weighs 0.315 N in air and 0.285 N when it hangs fully in water…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

An old coin weighs $0.315\ \text{N}$ in air and $0.285\ \text{N}$ when it hangs fully in water. Find its relative density. Silver has a relative density of $10.5$ and copper $8.9$ . Which is it more likely to be?

Need a reminder? The key ideaShow

Archimedes' principle: the buoyant force equals the weight of fluid pushed aside, $F_B = \rho_f V_{\text{under}}\,g$ . A body floats if it is less dense than the fluid, with the fraction $\dfrac{\rho_b}{\rho_f}$ of its volume under. Relative density $= \dfrac{W_{\text{air}}}{W_{\text{air}} - W_{\text{water}}}$ .

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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