Which of the following cylindrical rods will conduct the most heat when their ends are maintained at the same steady temperatures?

The electrostatic potential inside a charged spherical ball is given by $\phi = ar^2 + b$,where $r$ is the distance from the centre and $a, b$ are constants. Then the charge density inside the ball is

$A$ particle moving with a uniform acceleration travels $24 \,m$ and $64 \,m$ in the first two consecutive intervals of $4 \,sec$ each. Its initial velocity is............$m/sec$.

The fundamental frequency of a sonometer wire is $n$. If the length,tension,and diameter of the wire are all tripled,what is the new fundamental frequency?

$\lim _{x \rightarrow 0} \left( \frac{x \cdot 10^x - x}{1 - \cos x} \right)$ is equal to

$A$ $U$-tube has a left limb with a cross-sectional area that is one-quarter of the right limb. The tube contains mercury (density $13.6 \ g/cm^3$). The level of mercury in the narrow left limb is at a distance of $36 \ cm$ from the upper end of the tube. What will be the rise in the level of mercury in the right limb if the left limb is filled to the top with water (in $cm$)? (Density of water = $1 \ g/cm^3$)