Question

The loss in weight of a solid when immersed in a liquid at 0${}^0$C is W${}_0$ and at t${}^0$ C is ‘W’. If cubical coefficient of expansion of the solid and the liquid are ${\gamma }_s$ and ${\gamma }_l$ then W=

• A. $W_0[1+({\gamma }_s-{\gamma }_l\left)t\right]$
• B. $W_0[1-({\gamma }_s-{\gamma }_l\left)t\right]$
• C. $W_0\left[\right({\gamma }_s-{\gamma }_l\left)t\right]$
• D. $\frac{W{t}_0}{{\gamma }_s-{\gamma }_l}$

Answer 1

The correct option is A $W_0[1+({\gamma }_s-{\gamma }_l\left)t\right]$

From Archimedes' Principle, loss in weight $=$ weight of the liquid displaced.

Change in volume of the solid with temperature $=V_0{\gamma }_{s}t$

New density of liquid at $t^{\circ }C$=$\frac{d_0}{1+{\gamma }_{l}t}$

$W_0=V_0{d}_{0}g$

$W_1=V_1{d}_{1}g=V_0(1+{\gamma }_{s}t)\frac{d_0}{1+{\gamma }_{l}t}g=\frac{W_0(1+{\gamma }_{s}t)}{(1+{\gamma }_{l}t)}\approx W_0[1+({\gamma }_s-{\gamma }_l\left)t\right]$