One end of a long iron chain of linear mass density λ is fixed to a sphere of mass m and specific gravity 1/3 . The sphere with the chain is immersed in a deep lake (Figure 5.132). The specific gravit

Question

One end of a long iron chain of linear mass density $λ$ is fixed to a sphere of mass $m$ and specific gravity $1/3$ . The sphere with the chain is immersed in a deep lake (Figure 5.132). The specific gravity of iron is 7. If the sphere is slightly displaced vertically from equilibrium, the time period of the resulting SHM is:

TestHub · Accepted Answer

Sphere net buoyant force = 3 m g − m g = 2 m g . Apparent weight of chain per length = 7 6 ​ λ g , so equilibrium lifted chain h = 3 λ 7 m ​ . Moving mass m + λh = 3 10 m ​ , restoring constant 7 6 λ g ​ . T = 2 π 6 λ g /7 10 m /3 ​ ​ = 3 2 π ​ λ g 35 m ​ ​ .

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