A beam balance has arms of unequal lengths (left) and (right)
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A beam balance has arms of unequal lengths l1 (left) and l2 (right). When a body of unknown mass m is placed in the left pan, it is found to be in equilibrium with standard weights of mass M placed in the right pan.
(i) State the condition for rotational equilibrium of the beam about its knife-edge.
(ii) Using this condition, derive an expression relating m, M, l1 and l2.
(iii) If the inequality of the arms is ignored in practice, obtain an expression for the percentage error committed in determining the mass of the body when l1=l2 but M is assumed to be correct.