$A$ beaker is filled completely with water at $4^{\circ} C$. Identify the incorrect statement.

The densities of wood and benzene at $0^{\circ} C$ are $880 \ kg \ m^{-3}$ and $900 \ kg \ m^{-3}$,respectively. The coefficients of volume expansion are $1.2 \times 10^{-3} \ ^{\circ}C^{-1}$ for wood and $1.5 \times 10^{-3} \ ^{\circ}C^{-1}$ for benzene. The temperature at which a piece of wood just sinks in benzene is (in $^{\circ} C$)

$A$ metal block is made from a mixture of $2.4 \ kg$ of aluminium,$1.6 \ kg$ of brass,and $0.8 \ kg$ of copper. The metal block is initially at $20^{\circ} C$. If the heat supplied to the metal block is $44.4 \ cal$,find the final temperature of the block if the specific heats of aluminium,brass,and copper are $0.216, 0.0917, 0.0931 \ cal \cdot kg^{-1} \cdot ^{\circ}C^{-1}$ respectively. (in $^{\circ} C$)

When $1\, g$ of water at $0^{\circ}C$ and $1 \times 10^5\, N/m^2$ pressure is converted into ice of volume $1.091\, cm^3$,the external work done will be (in $, J$)

$A$ copper ring has a diameter of exactly $25 \, mm$ at its temperature of $0^o C$. An aluminium sphere has a diameter of exactly $25.05 \, mm$ at its temperature of $100^o C$. The sphere is placed on top of the ring and the two are allowed to come to thermal equilibrium,with no heat being lost to the surroundings. The sphere just passes through the ring at the equilibrium temperature. The ratio of the mass of the sphere to the ring is: (Given: $\alpha_{Cu} = 17 \times 10^{-6} /^o C$,$\alpha_{Al} = 2.3 \times 10^{-5} /^o C$,specific heat of $Cu = 0.0923 \, cal/g^o C$,and specific heat of $Al = 0.215 \, cal/g^o C$)

$A$ pendulum clock (fitted with a small heavy bob that is connected with a metal rod) is $5 \ s$ fast each day at a temperature of $15 \ ^oC$ and $10 \ s$ slow at a temperature of $30 \ ^oC$. The temperature at which it is designed to give correct time is ........ $^oC$.