A hollow cylinder of mass 1 kg and length 0.5 m (base and lid massless) hangs as a pendulum bob. Liquid fills it to height x , with 2 kg of liquid per metre of height. For what x is the period maximum

Question

A hollow cylinder of mass 1 kg and length 0.5 m (base and lid massless) hangs as a pendulum bob. Liquid fills it to height x , with 2 kg of liquid per metre of height. For what x is the period maximum, in m?

TestHub · Accepted Answer

Maximum period when the centre of mass is at the liquid surface: λ x 2 + 2 M x − M h = 0 , i.e. 2 x 2 + 2 x − 0.5 = 0 . x = 4 − 2 + 8 ​ ​ = 0.207 m.

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