Physics

Question 1 (6 marks)
a) Newton’s universal law of gravitation describes the force of gravity acting on two masses. The
correct equation is,
Fg = G
m1m2
r
2
.
Using dimensional analysis, determine the dimensions and SI units for the gravitational constant
G. Here, Fg is a force, m1 and m2 are masses and r is a distance. (2 marks)
b) Someone then tells you that the equation for gravitational potential energy U (measured in
Joules) is,
U = −G
m1m2
r
3
.
Using dimensional analysis, determine if they are correct. (1 mark)
c) An experiment determined that the time for a star to orbit a black hole T in a circular orbit
depends on the distance from the black hole to the star r, the gravitational constant G and the
mass of the black hole m. That is,
T = CrαG
βmγ
where C is a dimensionless constant. Using only dimensional analysis, determine what the
exponents α, β and γ must be for this equation to be correct. (3 marks)
Question 2 (7 marks)
Answer the following given the two vectors written in standard position.
A⃗ = 4m/s @ 220o B⃗ = 7m/s @ 300o
a) Draw a diagram for A⃗ and write A⃗ in terms of ˆi and ˆj (answer to 2 decimal places). (2 marks)
b) Draw a diagram for B⃗ and write B⃗ in terms of ˆi and ˆj (answer to 2 decimal places). (2 marks)
c) Determine the angle θ between A⃗ and B⃗ using the dot product. Then draw a diagram and use