Questions
A brass cube of side a and density is floating in mercury of density . If the cube is displaced a bit vertically, it executes S.H.M. Its time period will be
detailed solution
Correct option is A
As a is the side of cube σ is its density. Mass of cube is a2σ, its weight =a3σgLet h be the height of cube immersed in liquid of density ρ in equilibrium then, F=a2h ρ g=Mg=a3σ gIf it is pushed down by y then the buoyant force F'=a2(h+y)ρ gRestoring force is ΔF=F'−F=a2(h+y)σ g−a2h σ g =a2y ρ gRestoring acceleration =ΔFM=−a2yρ gM=−a2ρ ga3σyMotion is S.H.M. ⇒T=2πa3σa2ρ g=2πaσρ gSimilar Questions
A sphere of radius r is kept on a concave mirror of radius of curvature R. The arrangement is kept on a horizontal table (the surface of concave mirror is frictionless and sliding not rolling). If the sphere is displaced from its equilibrium position and left, then it executes S.H.M. The period of oscillation will be
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