Show quantity independence

Questions that ask to show or prove that a quantity does NOT depend on a particular variable (e.g., showing that pendulum period T does not depend on mass m) using dimensional analysis.

1 questions · Moderate -0.5

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AQA M3 2006 June Q1
7 marks Moderate -0.5
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:
  1. show that \(T\) does not depend on \(m\);
  2. express \(T\) in terms of \(l , g\) and \(k\), where \(k\) is a dimensionless constant.