1 The time \(T\) taken for a simple pendulum to make a single small oscillation is thought to depend only on its length \(l\), its mass \(m\) and the acceleration due to gravity \(g\).
By using dimensional analysis:
- show that \(T\) does not depend on \(m\);
- express \(T\) in terms of \(l , g\) and \(k\), where \(k\) is a dimensionless constant.