When the elevator is at rest, the barometer reads 760 mm. This is because the atmospheric pressure is balanced by the weight of the column of mercury in the barometer, resulting in a reading of 760 mm.

When the elevator moves in the upward direction with increasing speed, the reading of the barometer will be less than 760 mm. This is because as the elevator moves upwards, it goes to a region with lower atmospheric pressure. In this new region, the pressure exerted on the barometer is less than the weight of the column of mercury, causing the reading to decrease.

Option 1: 760 mm – This is not the correct answer because the barometer reading will decrease when the elevator moves in the upward direction.

Option 3: > 760 mm – This is not the correct answer because the barometer reading will be less than 760 mm, not greater.

Option 4: Zero – This is not the correct answer because the barometer still measures the atmospheric pressure, even when the elevator is in motion.

Therefore, the correct answer is option 2: < 760 mm.