Answers:
x = x_{o} + v_{o} t + (1/2) a t^{2} | where x is the displacement at time t,
x_{o} is the displacement at time t = 0, vo is the velocity at time t = 0, a is the constant acceleration |
Dimensionally correct. Each term has dimensions of L. |
P = | where P is pressure,
r is density, g is gravitational acceleration, h is height |
Not dimensionally correct.
[P] = M·L^{-1}·T^{-2} [] = M^{1/2}·L^{-1/2}·T^{-1} |
ln N_{d}/N_{a} = - [ Vgh_{d}(r - r_{l})] / kT | where N_{d} and N_{a} are number of
particles, V is volume, g is gravitational acceleration, h_{d} is distance, r and r_{l} are densitites, k is Boltzmann's constant with SI units of joules per kelvin, T is absolute temperature. |
Dimensionally correct. Left side of the equation is
"dimensionless".
[Vgh_{d}(r-r_{l})] = M·L^{2}/T^{2}. kT has SI units of joules, (which is a unit of energy), and therefore [kT] = M·L^{2}/T^{2}. Right side of the equation is also "dimensionless", since (M·L^{2}/T^{2})/(M·L^{2}/T^{2}) =1. |