A spherical ball of radius $1$ mm and density $10.5$ g/cc is dropped in glycerine of coefficient of viscosity $9.8$ poise and density $1.5$ g/cc. Viscous force on the ball when it attains constant velocity is $3696 \times 10^{-x}$ N. The value of $x$ is
(Given, $g = 9.8 \text{ m}/\text{s}^2$ and $\pi = \dfrac{22}{7}$)

A vessel contains oil (density $= 0.8 \text{ gm}/\text{cm}^3$) over mercury (density $= 13.6 \text{ gm}/\text{cm}^3$). A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in $\text{gm}/\text{cm}^3$ is

Three identical heat conducting rods are connected in series as shown in the figure. The rods on the side have thermal conductivity $2K$ while that in the middle has thermal conductivity $K$. The left end of the combination is maintained at temperature $3T$ and the right end at $T$. The rods are thermally insulated from outside. In steady state, temperature at the left junction is $T_1$ and that at the right junctions is $T_2$. The ratio $T_1/T_2$ is

A wire of length $L$ and diameter $d$ is used in a bulb. The temperature of wire is $T$ and power radiated by the wire is $P$. Its emissivity is ($\sigma$ = Stefan's constant) (Assume that emissivity of wire material is same at all wavelength)