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Question: Density of ice is \(\rho\) and that of water is \(\sigma\). What will be the decrease in volume when...

Density of ice is ρ\rho and that of water is σ\sigma. What will be the decrease in volume when a mass M of ice melts?

A

(a) Mσ−ρ\frac{M}{\sigma - \rho}

A

(b) σ−ρM\frac{\sigma - \rho}{M}

A

(c) M[1ρ−1σ]M\left\lbrack \frac{1}{\rho} - \frac{1}{\sigma} \right\rbrack

A

(d) 1M[1ρ−1σ]\frac{1}{M}\left\lbrack \frac{1}{\rho} - \frac{1}{\sigma} \right\rbrack

Explanation

Solution

(c)

Volume of ice =Mρ= \frac{M}{\rho}, volume of water =Mσ= \frac{M}{\sigma}

∴ Change in volume =Mρ−Mσ=M(1ρ−1σ)= \frac{M}{\rho} - \frac{M}{\sigma} = M\left( \frac{1}{\rho} - \frac{1}{\sigma} \right)