Is an allene or a conjugated diene formed? If we dehydrate the following molecule, which hydrogen ($\ce{H1}$ or $\ce{H2}$) gets removed?



The conclusion that I have drawn from the molecule: The carbon to which $\ce{H1}$ is attached is $\ce{sp2}$ hybridized which makes $\ce{H1}$ slightly more acidic than $\ce{H2}$.
As the intermediate passes through an allylic carbocation which is fairly stable, it does not matter which H is 'more acidic' - the whole system is in equilibrium. The product you get is the thermodynamically most stable which will be a conjugated diene.