The value of poisson's ratio lies between......... (A) - 1 to \((1 / 2)\) (B) \(-(3 / 4)\) to \([(-1) / 2]\) (C) \(-(1 / 2)\) to 1 (D) 1 to 2

Poisson's ratio, denoted by ν (nu), is a measure of how a material deforms under stress. Its values range from -1 to 0.5 for most materials. Simply put, Poisson's ratio is always between -1 and 0.5.

Here are the given options: (A) - 1 to \((1 / 2)\) (B) \(-(3 / 4)\) to \([(-1) / 2]\) (C) \(-(1 / 2)\) to 1 (D) 1 to 2 Now, we simply need to determine which of these options fits within the known range of Poisson's ratio. (A) This option has the correct range, which is from -1 to 0.5. (B) The lower limit is correct, but the upper limit is incorrect. If this were the correct range, it would mean that Poisson's ratio could never be between -0.5 and 0.5, but we know from our understanding of the material property that this is not true. (C) The lower limit is incorrect, as Poisson's ratio can be between -1 and -0.5. The upper limit is also incorrect, as we know that the upper limit of Poisson's ratio is 0.5, not 1. (D) This range is entirely outside the known range of Poisson's ratio, so it is not the correct answer.

Comparing all given options to the known range of Poisson's ratio, we find that option (A) is the correct answer. The value of Poisson's ratio lies between -1 and \((1 / 2)\).