When a meter rod made of silver at $0^{\circ} C$ is heated to $100^{\circ} C$,its length increases by $0.19 \ cm$. Find the coefficient of volume expansion of the silver.

The moment of inertia $I$ of a uniform rod about a perpendicular bisector increases to $I+\Delta I$,if the temperature is increased slightly by $\Delta T$. If the coefficient of linear expansion is $\alpha$,then $\frac{\Delta I}{I}$ is (Assume $\frac{\Delta T}{T} \ll 1$)

$A$ steel meter scale is to be ruled so that millimeter intervals are accurate within about $5 \times 10^{-5} \,m$ at a certain temperature. The maximum temperature variation allowable during the ruling is (Coefficient of linear expansion of steel $= 10 \times 10^{-6} \,K^{-1}$) (in $^{\circ} C$)

Two rods,one of aluminum and another of steel,have initial lengths $l_1$ and $l_2$ respectively. They are joined together to form a single rod of length $(l_1 + l_2)$. If the coefficients of linear expansion for aluminum and steel are $\alpha_a$ and $\alpha_s$ respectively,and the increase in length for both rods is the same when the temperature of both is increased by $t \ ^\circ C$,then $\frac{l_1}{l_1 + l_2} = \dots$

$A$ blacksmith fixes a circular iron frame on the wooden wheel of a bullock cart. The diameters of the wooden wheel and the circular iron frame are $5.012 \ m$ and $5 \ m$ respectively at $27^{\circ} C$. The temperature (in $^{\circ} C$) to which the iron ring must be heated so as to fit the wooden wheel is (Coefficient of linear expansion of iron $= 1.2 \times 10^{-5} \ ^{\circ} C^{-1}$).

$A$ clock which keeps correct time at $20^{\circ} C$,is subjected to $40^{\circ} C$. If the coefficient of linear expansion of the pendulum is $12 \times 10^{-6} /{ }^{\circ} C$,how much time will it gain or lose per day?