When driving my 2000 yr v8 4.0 she rangerover petrol there is a whining noise from the back end only when I let foot off accelerater , and a slight click when starting off from traffic lights

SOURCE: 2003 differential whine/noise

The last time I had a hum coming out of the area of the differential it was an inside axle bearing going bad. In my case there were four bearings (one on each end of each axle). It was a Toyota. We changed one bearing after listening very carefully and guessed right. I don't know if Cadillac is built similar in this regard but I'm thinking it may be. It was a speed sensitive hum sound like you describe.

SOURCE: whine from rear end

Sounds like a pinion bearing or rear axle shaft bearing.

SOURCE: whining noise from front end. starts at 5mph and

Hi,
If the sound is coming from your power steering pump and the fluid level is good, the pump could be going out.

SOURCE: Have a whining noise coming

that sounds right

SOURCE: my 52 mini suddenly started making a whining

Check your transmission fluid level, as recommended in the Owner's Manual. Also, if your car is equipped with power steering, check the fluid level in the power steering reserve.

If all fluids are at recommended levels, see if you can locate the noise. If it is in the engine compartment, try to determine if the noise is coming from any of the serpentine belt pulleys.

Sometimes the bearings on air injector pumps fail in higher-mileage vehicles, first causing a "whining" noise, and ultimately resulting in the serpentine belt "chirping" or squealing on acceleration. Best you can do is make sure all fluids are at recommended levels, then try to pinpoint the source of the whining noise for further diagnosis.

Hope that's helpful!.