The torque produced by a force acting on a lever arm can be given by the formula , where F is the force, r is the length of the lever arm, and k is a dimensionless constant. Using dimensional analysis, the value of the exponent a is found to be:
1
2
3
4
The torque can be expressed in terms of force, length and time as , which has dimensions of
. Using dimensional analysis, we can write
, where k is a dimensionless constant and a is the unknown exponent. Equating the dimensions on both sides, we get
. Equating the dimensions of force and length, we get a+1=1, which gives a=0. Therefore, the value of a is 1.