Units and Measurement Questions and Answers

Answer: E

The correct statement is (2) and (3) are four.

In 5.600 all digits count: the 5, the 6 and the two trailing zeros after the decimal point, which are significant. In 0.07200 the leading zeros only fix the decimal point and do not count, leaving 7, 2, 0, 0: four significant figures.

For 25300 the trailing zeros of a whole number without a decimal point are not taken as significant, so it has three, not five. (2) is not two and (3) is not three, and (1) does not have four.

Answer: B

The mismatch is Torque : \(\mathrm{ML^{2}T^{-1}}\).

Torque is force times distance, so its dimensions are \(\mathrm{MLT^{-2}} \times \mathrm{L} = \mathrm{ML^{2}T^{-2}}\), the same as energy. \(\mathrm{ML^{2}T^{-1}}\) is the dimension of angular momentum.

The others are correct: force \(\mathrm{MLT^{-2}}\); pressure, force per area, \(\mathrm{ML^{-1}T^{-2}}\); heat energy \(\mathrm{ML^{2}T^{-2}}\); thermal conductivity, from \(\frac{Q}{t} = kA\frac{\Delta T}{x}\), \(\mathrm{MLT^{-3}K^{-1}}\).

Answer: B

EMF is measured in volts.

Electromotive force is the energy a source such as a cell or generator gives each coulomb of charge that passes through it. Energy per unit charge, joules per coulomb, is the volt, the same unit as potential difference.

The ohm is the unit of resistance, the ampere of current and the watt of power, so none of them can measure an electromotive force.

Answer: C

The error in e was 0.6%.

For a power law \(e = K\eta^{n}\) with K exact, relative errors scale by the exponent:

\[ \begin{aligned} \frac{\delta e}{e} &= n\frac{\delta\eta}{\eta} \\ &= 1.5 \times 0.4\% = 0.6\% \end{aligned} \]

Since \(\eta\) was too low, e came out about 0.6% too low. 0.4% ignores the exponent, 1.5% confuses the exponent with the error, and 0.7% has no basis.

Answer: B

The percentage error in velocity is 2%.

For a product of powers, the relative errors add, each multiplied by its power. With K = \(\frac{1}{2}mv^{2}\):

\[ \begin{aligned} \frac{\Delta K}{K} &= \frac{\Delta m}{m} + 2\frac{\Delta v}{v} \\ 7 &= 3 + 2x \\ x &= 2\% \end{aligned} \]

4% is the result of forgetting to divide by the power 2, and 1% or 3% do not satisfy the equation.