Emotional Development
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Consider the following statements regarding physical quantities, their dimensional formulas, and measurement methods:
- 1. The dimensional formula of the Coefficient of Viscosity is $[ML^{-1}T^{-1}]$, and its SI unit is pascal-second ($Pa\cdot s$) or kilogram per meter-second ($kg \cdot m^{-1} \cdot s^{-1}$).
- 2. Both Planck's Constant and Angular Momentum have exactly the same dimensions, and the dimensional formula for both is $[ML^2T^{-1}]$.
- 3. When calculating the error in the measurement of a physical quantity, if a quantity is related in the form $X = \frac{A^2 B^3}{C}$, then the value of the maximum fractional error in that quantity is $\frac{\Delta X}{X} = 2\left(\frac{\Delta A}{A}\right) + 3\left(\frac{\Delta B}{B}\right) - \left(\frac{\Delta C}{C}\right)$.
- 4. Both Light Year and Parsec are units of measuring astronomical distances, where the value of 1 Parsec is approximately equal to $3.26$ Light Years.
Which of the above statement(s) is/are completely true?
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Detailed Explanation
According to the precise analysis of this question, statements 1, 2, and 4 are completely true. The dimensional formula of the coefficient of viscosity is $[ML^{-1}T^{-1}]$ and its unit is $Pa\cdot s$. Planck's constant ($E = h\nu$, where the dimension of $h$ is $[ML^2T^{-1}]$) and angular momentum ($L = mvr$, whose dimension is also $[ML^2T^{-1}]$) have the same dimensions. Parsec and light-year are both units of distance and 1 Parsec = 3.26 Light-years. Statement 3 is false because there is no negative sign in error analysis; while finding the maximum possible error, all errors are always added, i.e., $\frac{\Delta X}{X} = 2\left(\frac{\Delta A}{A}\right) + 3\left(\frac{\Delta B}{B}\right) + \left(\frac{\Delta C}{C}\right)$.
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