A uniform taut string with two point charges $q$ and $-q$ attached to its ends passes over two massless pullies kept $L$ distance apart as shown in the fgure. If $f$ is the fundamental frequency of the part of the string over pullies, which of the following statements is correct?

Two uniformly charged concentric thin spherical shells of radii $r_1$ and $r_2$ have charges $+Q$ and $-Q$, respectively. How does the electrostatic potential vary with distance from the center of the shells?

Consider a very long cylinder of radius $a$ having a uniform positive charge density $\rho$. A sphere of radius $a$ has been carved out (see figure), leaving no charge in that region. The distance radially outward to the cylinder, as measured from the center of the sphere is $x$. At what value of $x$ will the electric field be maximum?

Consider that in a fission of a single Plutonium ( $\mathrm{Pu}^{239}$ ) atom 207 MeV energy is released. Assuming all atoms of Plutonium undergo fission, which of the following options is the closest estimate of the amount of Plutonium required for a 20,000 units of TNT explosion? (1 unit of TNT $=4.184 \times 10^9 \mathrm{~J}, 1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J}$ )