(a)[3]
Show that the cross-sectional area $A$ of the cylinder is $0.016\,\text{m}^2$.
(b(i))[1]
Show that the upthrust acting on the cylinder due to the liquid is $32\,\text{N}$.
(b(ii))[3]
Calculate the density of the liquid.
(c(i))[3]
Fig. 1.3 displays how the tension $F$ changes with the length of the spring in (b). The tap at the base of the container is opened so that a fixed amount of liquid leaves the container. The cylinder then moves downwards so that the tension in the spring changes from $8.0\,\text{N}$ to $4.0\,\text{N}$. Determine the change in the elastic potential energy of the spring.
(c(ii))[1]
Additional liquid is drained from the container until the upthrust on the cylinder is reduced to $24\,\text{N}$. For an upthrust of $24\,\text{N}$, determine the length of the spring.