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Q.

A body suspended from a spring balance is immersed in water. If the coefficient of cubical expanison of water is twice that of the suspended body, then on heating the liquid, which one of the following would occur ?

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a

The reading on the spring balance decreases

b

The water flows out of the container

c

The reading on the spring balance remains the same

d

The reading on the spring balance increases

answer is A.

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Detailed Solution

If W be the true weight of the body and B₀ be the initial buoyant force, then initial reading , W₁ = W-B₀ . On heating new buoyant force becomes $\large {B^1}_0\, = \,{B_o}\left[ {1 - \left( {{\gamma _\rho } - {\gamma _s}} \right)\Delta s} \right]$

$\large {B^1}_0\, = \,{B_o}\left[ {1 - \left( {2\gamma - \gamma } \right)\Delta t} \right]$

$\large \Rightarrow \,{B^1}_0\, = \,{B_o}\left[ {1 - \gamma .\Delta t} \right]$

$\large \therefore$ Final reading, $\large {W_2}\, = \,W - {B^1}_o$

Since $\large {B^1}_o\, < \,{B_o}$ , we conclude W₂ > W₁

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