A cylindrical metal rod of length $L_0$ is shaped into a ring with a small gap as shown. On heating the system
$x$ decreases, $r$ and $d$ increase
$x$ and $r$ increase, $d$ decreases
$x$, $r$ and $d$ all increase
Data insufficient to arrive at a conclusion
An open vessel is filled completely with oil which has same coefficient of volume expansion as that of the vessel. On heating both oil and vessel,
A one litre glass flask contains some mercury. It is found that at different temperatures the volume of air inside the flak remains the same. ...... $cc$ is the volume of mercury in this flask if coefficient of linear expansion of glass is $9 \times 10^{-6} /^o C$ while of volume expansion of mercury is $1.8 \times {10^4}\,/^\circ C$
Two rods, one of aluminum and the other made of steel, having initial length ${l_1}$ and ${l_2}$ are connected together 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 length of each rod increases by the same amount when their temperature are raised by ${t^o}C$, then find the ratio $\frac{{{l_1}}}{{({l_1} + {l_2})}}$
Calculate the stress developed inside a tooth cavity filled with copper when hot tea at temperature of $57\,^oC$ is drunk. You can take body (tooth) temperature to be $37\,^oC$ and $\alpha = 1.7 \times 10^{-5}/^oC$, bulk modulus for copper $ = 140 \times 10^9\, N/m^2 $.
Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures $T _1=300 K$ and $T _2=100 K$, as shown in the figure. The radius of the bigger cylinder is twice that of the smaller one and the thermal conductivities of the materials of the smaller and the larger cylinders are $K _1$ and $K _2$ respectively. If the temperature at the junction of the two cylinders in the steady state is $200 K$, then $K _1 / K _2=$ . . . . .