1. What types of natural phenomena could serve as time standards?
Ans: Atomic clocks are based on electromagnetic waves which atoms emit. Also, pulsars are highly regular astronomical clocks.
2. Supposed the three fundamental standards of the metric system were length, density, and time rather than length, mass, and time. The standard of density in this system is to be defined as that of water. What considerations about water would you need to address to make sure that the standard of density is as accurate as possible?
Ans: Density varies with temperature and pressure. It would be necessary to measure both mass and volume very accurately in order to use the density of water as a standard.
3. Suppose two quantities A and B have different dimensions. Determine which of the following arithmetic operations could be physically meaningful: (a) A + B, (b) $\frac{A}{B}$, (c) B – A, (d) AB.
Ans: (b) and (d). You cannot add or subtract quantities of different dimension.
4. If an equation is dimensionally correct, does that mean that the equation must be true? If an equation is not dimensionally correct, does that mean that the equation cannot be true?
Ans: A dimensionally correct equation need not be true. Example: 1 monkey = 2 monkey is dimensionally correct. However, if an equation is not dimensionally correct, it cannot be correct.
5. What level of precision is implied in an order-of-magnitude calculation?
Ans: Zero significant digits. An order-of-magnitude calculation is accurate only within a factor of 10.
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