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Question

# Ratio of the weights of a 1 kg block of iron and 1 kg block of wood as measured by a spring balance is: Given: Density of iron =7800 kg/m3, density of wood =800 kg/m3 and density of air =1.293 kg/m3

A
1.5
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B
2.0015
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C
1.0015
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D
3.0015
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Solution

## The correct option is C 1.0015FBD of the block: Applying equilibrium condition i.e ∑F=0 along vertical direction. Considering air as a fluid, it will exert buoyant force on block. ⇒T+Fb−mg=0 ⇒T=mg−Fb ⇒T=mg−ρagV ...(1) [ρa→density of air] From Eq.(i) for iron block: T1=mg−ρagVi where Vi→ volume of iron block ⇒T1=(1×10)−1.293×10×17800 [∵Vi=mρi] ⇒T1=9.9983 N Similarly, for wooden block , T2=mg−ρagVw [Vw=mρw] ⇒T2=(1×10)−1.293×10×1800 ⇒T2=9.9838 N On dividing T1 & T2, T1T2=9.99839.9838 ∴T1:T2=1.0015 Ratio of weights of iron and wooden block of mass 1 kg is 1.0015.

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