Question

Whenever a liquid is heated in a container, expansion in liquid as well as container takes place. If r is the volume expansion coefficient of liquid and is coefficient of liner expansion. Match the entries of Column I and Column II
$$\begin{array}{cc}ColumnI& ColumnII\\ \left(i\right)Liquidlevelriseswithrespecttocontainer& \left(A\right)g=2a\\ \left(ii\right)Liquidlevelremainssamewithrespecttocontainer& \left(B\right)2\alpha <\gamma <3\alpha \\ \left(iii\right)Liquidleveldropswithrespecttocontainer& \left(C\right)g=3a\\ \left(iv\right)Liquidlevelremainssamewithrespecttoground& \left(D\right)g>3a\end{array}$$

• A. (i) - (D), (ii) – (C), (iii) – (B), (iv) – (A)
  
• B. (i) - (A), (ii) – (C), (iii) – (B), (iv) – (D)
  
• C. (i) - (B), (ii) – (C), (iii) – (D), (iv) – (A)
  
• D. (i) - (D), (ii) – (A), (iii) – (B), (iv) – (C)
  

Answer 1

The correct option is A (i) - (D), (ii) – (C), (iii) – (B), (iv) – (A)

Change in volume of a liquid w.r.t. container
$\Delta V=V_0[\gamma -3\alpha ]\Delta T$
$\alpha$ = co-effecient of linear exparosion of material of container and $\gamma$ is volume expansion co-effecient of liquid
(a) If $\gamma >3\alpha$ level of liquid rises w.r.t. container as well as w.r.t. ground
(b) $\gamma =3\alpha$ level of liquid remains same w.r.t. container but rises w.r.t. ground
(c) $3\alpha >2\alpha$ level of liquid falls w.r.t. container but rise w.r.t. ground
(d) $\gamma >2\alpha$ level of liquid falls w.r.t. container but remains same w.r.t. ground