1.   Is the equation below homogeneous with respect to its units?

    x = ut + 1/2at²

2.   The velocity of a body of mass m that has been acted upon by a force F for a time t is given by Ft=mv. Show that this equation is dimensionally correct.

1 kilowatt hour is the same as:
A 1/3.6 J B 3.6 J C 1000 J D 3.6 x 10⁶ J

The mass of an object is measured to be 4.652 kg and its volume 2.1 m³. If the density (mass per unit volume) is calculated from these values, to how many significant figures should it be expresses?
A 1 B 2 C 3 D 4

Explain what is meant by the method of dimensions.
Point out the uses of the method, and its limitations. (6 marks)

Based on Newton's law of gravitation, define the universal gravitational constant G. (2 marks)
Use your definition to derive:
(i) the SI unit of G; (3 marks)
(ii) the dimensions of G. (2 marks)

An electromagnetic wave propagates in free space at a speed c given by the relationship
c = sq root (1/E₀U₀),
where E₀ and U₀ are respectively the permittivity and permeability of free space.
(i) Express the units of E₀ and U₀ (Fm^-1 and Hm^-1 respectively) in terms of the dimensions of length (L), mass (M), time (T) and current (I). (4 + 4)
(ii) Use the method of dimensions to establish the validity of the expressions for c given above. (4)