Determine the dimensions of the speed of light (c), Planck's constant (h), and the gravitational constant (G).

Here are the shortened solutions for the questions in the image:

Question 13:

Step 1: Determine the dimensions of each constant.

• A) Speed of light (c): $[L T^{-1}]$
• B) Planck's constant (h): Energy = h $\times$ frequency $\Rightarrow h = \frac{\text{Energy}}{\text{frequency}} = \frac{[M L^2 T^{-2}]}{[T^{-1}]} = [M L^2 T^{-1}]$
• C) Gravitational constant (G): $F = G \frac{m_1 m_2}{r^2} \Rightarrow G = \frac{F r^2}{m_1 m_2}