    Question

# A solid cube floats in water half immersed and has small vertical oscillations of time period π5s. Its mass (in kg) is: (Take g=10 ms−2)

A
4
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B
2
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C
1
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D
0.5
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Solution

## The correct option is A 4Given, Time period of oscillation (T)=π5s Density of liquid (ρ)=1000kg/m3 Since, cube is half immersed i.e h=l2 is the height of cube exposed above water surface. Applying the formula for floatation, hl=σρ where, l→ edge length of with cubical block σ→ Density of block ρ→ density of liquid ⇒l2×l=σρ ⇒σ=ρ2 i.e density of cube is half the density of liquid ⇒σ=500 kg/m3 Time period of oscillations is given as, ⇒T=2π√mρAg ....(i) Where m=σl3=mass of cubical block A=l2=cross-sectional area of cubical block Eq.(i) can be expressed as, ⇒T=2π√σlρg Substituting σρ=12 ⇒π5=2π√l2g ⇒l20=1100 (or)l=0.2 m Now mass of cube is, m=V×σ=l3σ=(0.2)3×500 ⇒m=4 kg  Suggest Corrections  5      Similar questions
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