To increase the length of a metal rod by $0.4 \%$, the temperature of the rod is to be increased by (Coefficient of linear expansion of the metal $= 20 \times 10^{-6} \ {}^{\circ}C^{-1}$) (in $K$)

$A$ clock pendulum made of invar has a period of $0.5 \, s$ at $20^{\circ} C$. If the clock is used in a climate where the temperature averages to $30^{\circ} C$, how much time does the clock lose in each oscillation? (For invar, $\alpha = 9 \times 10^{-7} /{ }^{\circ} C$, $g = \text{constant}$)

Three rods of equal lengths are joined to form an equilateral triangle $ABC$. $D$ is the mid-point of $AB$. The coefficient of linear expansion is $\alpha_1$ for the material of rod $AB$ and $\alpha_2$ for the material of rods $AC$ and $BC$. If the distance $DC$ remains constant for small changes in temperature, then:

If the length of a cylinder on heating increases by $2\%$,the area of its base will increase by ....... $\%$

When a copper ball is heated,the largest percentage increase will occur in its

$A$ piece of metal has a weight of $49 \ gm$ in air and $39 \ gm$ in a liquid of density $1.2 \times 10^3 \ kg/m^3$ kept at $32^{\circ}C$. When the temperature of the liquid is raised to $42^{\circ}C$, the metal piece has a weight of $40 \ gm$. If the density of the liquid at $42^{\circ}C$ is $1.0 \times 10^3 \ kg/m^3$, then the coefficient of linear expansion of the metal is: