Question

The period of swing of a simple pendulum depends on length L, mass M of the bob and acceleration due to gravity g. Using given by T = Kl^x m ^y g ^ z where k is a non dimensional constant. Use the method of dimension to find the values of x, y, z.

Answer 1

$$[T ]=[ K][l]^x [m] ^y [g] ^ z \\ T=L^xM ^y (LT^{-2}) ^ z\\ y=0\\z=-\frac{1}{2}\\x=-z=\frac{1}{2}$$