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- Lithium forms the normal oxide ($Li_{2}O$).
- Sodium forms the peroxide ($Na_{2}O_{2}$).
- Potassium (and larger alkali metals) forms the superoxide ($KO_{2}$).
A stone is dropped from rest from the top of a $20\text{ m}$ tower. Its speed on hitting the ground is ($g = 10\text{ m/s}^2$):
Using $v^2 = u^2 + 2gh = 0 + 2(10)(20) = 400$
$v = \sqrt{400} = \mathbf{20\text{ m/s}}$
What are the dimensions of the magnetic field $B$ in terms of $C$ (coulomb), $M$, $L$, and $T$?
From the Lorentz force: $F = qvB$
$[B] = \dfrac{[F]}{[q][v]} = \dfrac{MLT^{-2}}{C \cdot LT^{-1}} = MT^{-1}C^{-1} = M^1L^0T^{-1}C^{-1}$
Let $n$ be a positive integer divisible by 6. Compare:
Quantity A: The remainder when $n$ is divided by 12
Quantity B: The remainder when $n$ is divided by 18
Since $n$ is divisible by 6, $n$ can be $6, 12, 18, 24, 30, 36, \ldots$
Example 1: $n = 12$. Remainder ÷12 $= 0$. Remainder ÷18 $= 12$. B > A.
Example 2: $n = 18$. Remainder ÷12 $= 6$. Remainder ÷18 $= 0$. A > B.
Example 3: $n = 36$. Remainder ÷12 $= 0$. Remainder ÷18 $= 0$. Equal.
The relationship changes, so it cannot be determined.
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