Question

The factors affecting the time period (T) of a simple pendulum of mass (m) of the bob length (L) of the pendulum and the acceleration due to gravity (g).

Deduce a relation for 'T' in terms of 'm','L' and 'g'?

Answer 1

$\left[T\right]=\left[m{]}^a\right[L{]}^b[g{]}^c$

$\left[T\right]=k\left[m{]}^a\right[L{]}^b[L{T}^{-2}{]}^c$

$\left[T\right]=K\left[M{]}^a\right[L{]}^{b+c}[T{]}^{-2c}$

$a=0,b+c=0,-2c=1$
$b=-c$, $c=-\frac{1}{2}$

$T\infty \left[m{]}^a\right[L{]}^{1/2}[g{]}^{-1/2}$

$T=k\sqrt{\frac{L}{g}}$
$K=2\pi$
$T=2\pi \sqrt{\frac{L}{g}}$