A vertical column 50 cm long at $50^{c} i r c$ C balances another column of same liquid 60 cm long at $100^{c} i r c$ °C. The coefficient of absolute expansion of the liquid is

$0.005 /^{\circ} C$

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$0.0005 /^{\circ} C$

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$0.002 /^{\circ} C$

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$0.0002 /^{\circ} C$

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Solution

The correct option is A
$0.005 /^{\circ} C$

$\frac{h_{1}}{h_{2}} = \frac{ρ_{1}}{ρ_{2}} = \frac{(1 + γ θ_{1})}{1 + γ θ_{2}}$ $[∵ ρ = \frac{ρ_{0}}{(1 + γ θ)}]$

$\Rightarrow \frac{50}{60} = \frac{1 + γ \times 50}{1 + γ \times 100} \Rightarrow γ = 0.005 /^{\circ} C$

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A vertical column 50 cm long at 50circ C balances another column of same liquid 60 cm long at 100circ°C. The coefficient of absolute expansion of the liquid is

The correct option is A 0.005/∘C h1h2=ρ1ρ2=(1+γθ1)1+γθ2 [∵ρ=ρ0(1+γθ)] ⇒5060=1+γ×501+γ×100⇒γ=0.005/∘C

A vertical column 50 cm long at $50^{c} i r c$ C balances another column of same liquid 60 cm long at $100^{c} i r c$ °C. The coefficient of absolute expansion of the liquid is

The correct option is A
$0.005 /^{\circ} C$

$\frac{h_{1}}{h_{2}} = \frac{ρ_{1}}{ρ_{2}} = \frac{(1 + γ θ_{1})}{1 + γ θ_{2}}$ $[∵ ρ = \frac{ρ_{0}}{(1 + γ θ)}]$

$\Rightarrow \frac{50}{60} = \frac{1 + γ \times 50}{1 + γ \times 100} \Rightarrow γ = 0.005 /^{\circ} C$