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∕L^{2}M^{3} 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 mv
^{2}, 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 = mc
^{2}, 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 mc^{2}?M L2 L/M (M.L)/T M/(T2.L) L/T (M.L2)/(T2) (M.L)/(T2) L/(T2)