A glass tube of uniform cross-section is connected to a tap with a rubber tube. The tap is opened slowly. Initially the flow of water in the tube is streamline. The speed of flow of water to convert it into a turbulent flow is [radius of tube $$=1 \mathrm{~cm}, \eta=1 \times 10^{-3} \frac{\mathrm{Ns}}{\mathrm{m}^2}, R_n=2500$$ and density of water $$=10^3 \mathrm{~kg} / \mathrm{m}^3$$]

A sonometer wire of length 25 cm vibrates in unison with a tuning fork. When its length is decreased by 1 cm, 6 beats are heard per second. What is the frequency of the tuning fork?

The plates of a parallel plate capacitor of capacity '$$\mathrm{C}_1$$' are moved closer together until they ant half their original separation. The new capacitance '$$\mathrm{C}_2$$' is

A p-n junction photodiode is fabricated from a semiconductor with a band gap of $$2.5 \mathrm{~eV}$$. It can detect a signal of wavelength [Planck's constant $$=6.6 \times 10^{-34} \mathrm{Js}, \mathrm{c}=3 \times 10^8 \mathrm{~m} / \mathrm{s}, \mathrm{e}=1.6 \times 10^{-19} \mathrm{C}$$]