Physical Units. AGid

Physical quantities such as distance, velocity, and so on have specific dimensions. The dimensions of L, T, and M are fundamental, and other quantities have dimensions that are derived from these.

NOTE: To save space, dimensions such as T∕L2M3 are written as T/(L2.M3).

1.
What is the dimension of distance?
L  T  M  L2  L/M  (M.L)/T  M/(T2.L)  L/T  (M.L2)/(T3)/T/(L2)  L/(T2)
2.
Velocity is (change in) distance per unit time. What is the dimension of velocity?
L  T  M  L2  L/M  (M.L)/T  M/(T2.L)  L/T  (M.L2)/(T3)/T/(L2)  L/(T2)
3.
Momentum is velocity times mass. What is the dimension of momentum?
L  T  M  L2  L/M  (M.L)/T  M/(T2.L)  L/T  (M.L2)/(T3)/T/(L2)  L/(T2)
4.
Acceleration is (change in) velocity per unit time. What is the dimension of acceleration?
L  T  M  L2  L/M  (M.L)/T  M/(T2.L)  L/T  (M.L2)/(T2)  L/(T2)
5.
Force is acceleration times mass: F = MA is the famous formula. What is the dimension of force?
L/M  (M.L)/T  M/(T2.L)  L/T  (M.L2)/(T2)  (M.L)/(T2)  (M.L2)/(T3)  L/(T2)
6.
Kinetic Energy is often given as mv2, where m is the object’s mass and v is the object’s velocity. What is the dimension of kinetic energy?
L2  L/M  (M.L)/T  M/(T2.L)  L/T  (M.L2)/(T2)  (M.L)/(T2)  (M.L2)/(T3)  L/(T2)
7.
Potential energy of an object of mass m at a height of h with acceleration due to gravity of g is given by the formula mhg. What is the dimension of this potential energy?
L2  L/M  (M.L)/T  M/(T2.L)  L/T  (M.L2)/(T2)  (M.L)/(T2)  (M.L2)/(T3)  T/(L2)  L/(T2)
8.
Work is force times distance. What is the dimension of work? (Hint: you’ve already seen this dimension, but in another form.)
L2  L/M  (M.L)/T  M/(T2.L)  L/T  (M.L2)/(T2)  (M.L)/(T2)  (M.L2)/(T3)  L/(T2)
9.
Power is energy per time. What is the dimension of power?
L/M  (M.L)/T  M/(T2.L)  L/T  (M.L2)/(T2)  (M.L)/(T2)  (M.L2)/(T3)  T/(L2)  L/(T2)
10.
Pressure is force per unit area (as in pounds per square inch). What is the dimension of pressure?
L2  L/M  (M.L)/T  M/(T2.L)  L/T  (M.L2)/(T2)  (M.L)/(T2)  (M.L2)/(T3)  L/(T2)
11.
Einstein famously wrote E = mc2, a formula that relates the energy content of an object to its mass m and the speed of light c. What is the dimension of mc2?
M  L2  L/M  (M.L)/T  M/(T2.L)  L/T  (M.L2)/(T2)  (M.L)/(T2)  L/(T2)