At 0 $^{0}$ C the densities of a cork and a liquid in which the cork floats are $d_{1}$ and $d_{2}$ respectively. The coefficient of expansion for the material of the cork and the liquid are $γ$ and 100 $γ$ respectively. If the cork sinks when the temperature of the liquid is t $^{0}$ C then the ratio $\frac{d_{2}}{d_{1}}$

\frac{1 + 100 γ t}{1 + γ t}

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\frac{1 + γ t}{1 + 100 γ t}

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\frac{100 + γ t}{1 + γ t}

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\frac{1 + γ t}{100 + γ t}

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Solution

The correct option is D $\frac{1 + 100 γ t}{1 + γ t}$
Density of a substance at temperature 't' whose initial density at $0^{\circ} C$ is given is $\frac{d_{0}}{1 + γ Δ T}$ .
If the cork sinks in the liquid at $t^{\circ} C$ ,
$V d_{c o r k} g = V d_{l i q u i d} g$
$⟹ d_{c o r k} = d_{l i q u i d}$
$⟹ \frac{d_{1}}{1 + γ t} = \frac{d_{2}}{1 + 100 γ t}$

$\frac{d_{2}}{d_{1}} = \frac{1 + 100 γ t}{1 + γ t}$

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At 00C the densities of a cork and a liquid in which the cork floats are d1 and d2 respectively. The coefficient of expansion for the material of the cork and the liquid are γ and 100γ respectively. If the cork sinks when the temperature of the liquid is t0C then the ratio d2d1

The correct option is D 1+100γt1+γtDensity of a substance at temperature 't' whose initial density at 0∘C is given is d01+γΔT.If the cork sinks in the liquid at t∘C, Vdcorkg=Vdliquidg⟹dcork=dliquid⟹d11+γt=d21+100γtd2d1=1+100γt1+γt