If a cylinder is heated such that its length increases by $2\%$,then its base area will increase by ......... $(\%)$.

$A$ uniform metal bar of length $10 \ m$ with a crack at its midpoint is clamped between two rigid supports. The bar buckles upward due to a temperature rise of $40^{\circ} C$. If the coefficient of linear expansion of the metal is $2.5 \times 10^{-6} {}^{\circ} C^{-1}$,the maximum displacement of the midpoint of the bar is: (in $cm$)

$A$ pendulum clock loses $12\;s$ a day if the temperature is $40^{\circ}C$ and gains $4\;s$ a day if the temperature is $20^{\circ}C$. The temperature at which the clock will show correct time,and the coefficient of linear expansion $(\alpha)$ of the metal of the pendulum shaft are respectively:

Obtain the relation between the coefficient of volume expansion $(\alpha_V)$ and the coefficient of linear expansion $(\alpha_l)$.

Two metal plates $P$ and $Q$ of the same material are arranged as shown in the figure. If both the plates are uniformly heated through the same range of temperature,then

The side of a copper cube is $1 \ m$ at $0^{\circ} C$. What will be the change in its volume,when it is heated to $100^{\circ} C$? $[\alpha_{\text{copper}} = 18 \times 10^{-6} /^{\circ} C]$