A sonometer wire resonates with $4$ antinodes between the two bridges for a given tuning fork when $1$ kg mass is suspended from the wire. Using same fork, when mass M is suspended, the wire resonates producing $2$ antinodes between the two bridges. (Distance between the bridges as before) The value of M is

The fundamental frequency of sonometer wire is $50$ Hz for some length and tension. If the length is increased by $25\%$ by keeping the tension same, then the frequency change of second harmonic is

The number of lines of force originating from a point charge of $2 \times 8.85 \times 10^{-9}$ C in a medium of dielectric constant $10$ is ($\epsilon_0 = 8.85 \times 10^{-12}$ SI unit)

The potential difference that must be applied across the parallel and series combination of three identical capacitors such that the energy stored in them becomes the same. The ratio of potential difference in parallel to series combination is