A jet of water is striking at the centre of a curved vane moving with a uniform velocity in the direction of jet. For the maximum efficiency, the vane velocity is ________ of the jet velocity

The efficiency of a water turbine or vane is maximized when the vane velocity matches half of the jet velocity. This condition ensures that the maximum energy transfer occurs from the jet to the vane.

Let's analyze each option:

Option A: "One-half" - This is correct for achieving maximum efficiency. When the vane velocity is half of the jet velocity, it allows for optimal energy transfer from the jet to the vane.

Option B: "One-third" - This is incorrect. A vane velocity of one-third of the jet velocity does not maximize efficiency; it would result in lower energy transfer.

Option C: "Two-third" - This is incorrect. A vane velocity of two-thirds of the jet velocity is not optimal for maximum efficiency in energy transfer.

Option D: "Three-fourth" - This is incorrect. A vane velocity of three-fourths of the jet velocity is also not optimal for maximum efficiency.

Therefore, the correct answer is Option A: One-half.