Measurements and Units

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1. A student measures the length of a wire using a metre rule with a smallest division of 1 mm. The reading obtained is 25.4 cm. Which of the following statements is correct regarding the precision of this measurement?

   1. A The uncertainty is exactly 1 mm
   2. B The uncertainty is estimated to be ±0.05 cm
   3. C The measurement is accurate to 0.01 cm
   4. D The uncertainty is ±0.1 cm

2. Which of the following sets of quantities consists entirely of derived quantities?

   1. A Mass, Length, Time
   2. B Force, Energy, Power
   3. C Current, Temperature, Force
   4. D Length, Energy, Mass

3. A student uses a micrometer screw gauge to measure the diameter of a wire. The main scale reading is 3.5 mm and the circular scale reading is 18.0 divisions. If the zero error is +0.02 mm, what is the correct diameter of the wire in millimetres?

   1. A 3.70 mm
   2. B 3.66 mm
   3. C 3.64 mm
   4. D 3.68 mm

4. A student proposes the equation $v = u + at^2$ to describe the motion of a car, where $v$ is final velocity, $u$ is initial velocity, $a$ is acceleration, and $t$ is time. Which of the following statements is correct regarding the dimensional homogeneity of this equation?

   1. A The equation is dimensionally correct because all terms involve length and time.
   2. B The equation is dimensionally incorrect because $u$ and $v$ have different dimensions.
   3. C The equation is dimensionally correct because $a$ and $t$ are fundamental quantities.
   4. D The equation is dimensionally incorrect because the term $at^2$ has dimensions of length, not velocity.

5. The coefficient of viscosity, $\eta$, is defined by the equation $F = \eta A \frac{dv}{dx}$, where $F$ is force, $A$ is area, $v$ is velocity, and $x$ is distance. What are the fundamental dimensions of the coefficient of viscosity?

   1. A [M L T^{-1}]
   2. B [M L^{-1} T^{-1}]
   3. C [M L^{-2} T^{-1}]
   4. D [M L^{-1} T^{-2}]

6. A physics student measures the diameter of a copper wire using a micrometer screw gauge. The main scale reading is 2.5 mm and the circular scale reading is 37.5 divisions. Given that the least count of the instrument is 0.01 mm, what is the measured diameter of the wire?

   1. A 2.537 mm
   2. B 2.875 mm
   3. C 2.875 cm
   4. D 2.500 mm

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