When a body is heated, then the maximum rise will be in its

Two rods are joined between fixed supports as shown in the figure. The condition for no change in the total length of the system with an increase in temperature is given by:
($\alpha_1, \alpha_2$ = linear expansion coefficients,$A_1, A_2$ = cross-sectional areas of rods,$Y_1, Y_2$ = Young's moduli)

In a thermostat, two metal strips are used, which have different ............

$A$ 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 the correct time is: (in $^{\circ} C$)

$A$ solid metal sphere has a spherical cavity inside it. If the sphere is heated,the volume of the cavity will.....

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