Answer to Question #98138 in Mechanics | Relativity for Hi

Question

a small mass is suspended from a long thread so as to form a simple pendulum. the period T of oscillation depends on the m the length L of the thread and the acceleration g of free fall at the place concerned T= KM^x L^y G^z where x,y,z are unknown and K =211 (1) Find the values of X Y Z (2) Hence derive an expression relating T M G and L

Answer 1

$$T= km^x l^y g^z$$

$$[T]= [m]^x [l]^y [g]^z$$

$$T= [M]^x [L]^y [LT^{-2}]^z$$

$$-2z=1\to z=-\frac{1}{2}$$

$$y-z=0\to y=\frac{1}{2}, x=0$$

Thus,

$$T=2\pi\sqrt{\frac{l}{g}}$$