Question

How this equation can be shown as dimensionally consistent T=2π√l/g

Answer 1

units of time,T are in seconds
since units of length of pendulum,l are in metre and acceleration due to gravity,g are in metre per second squared
=> length/length per time squared = time squared
due to the square root on RHS the time squared becomes 'time'
since 2(pie) is a constant it doesn't have any dimensions
therefore it can be shown that dimensions on LHS is equal to dimensions on RHS and the given eqn is dimensionally consistent

Answer 2

It is a linear equation (which shows consistency).

Answer 3

k= 2\[pi\]