JEE Advanced 2020 — Set 2

A large square container with thin transparent vertical walls and filled with water (refractive index 4 3) is kept on a horizontal table. A student holds a thin straight wire vertically inside the water 12 cm from one of its corners, as shown schematically in the figure. Looking at the wire from this corner, another student sees two images of the wire, located symmetrically on each side of the line of sight as shown. The separation (in cm) between these images is ____________.

A train with cross-sectional area 𝑆𝑡 is moving with speed 𝑣𝑡 inside a long tunnel of cross-sectional area 𝑆0 (𝑆0 = 4𝑆𝑡). Assume that almost all the air (density ρ) in front of the train flows back between its sides and the walls of the tunnel. Also, the air flow with respect to the train is steady and laminar. Take the ambient pressure and that inside the train to be 𝑝0. If the pressure in the region between the sides of the train and the tunnel walls is 𝑝, then 𝑝0 −𝑝= 7 2𝑁𝜌𝑣𝑡 2. The value of 𝑁 is ________.

Two large circular discs separated by a distance of 0.01 m are connected to a battery via a switch as shown in the figure. Charged oil drops of density 900 kg m−3 are released through a tiny hole at the center of the top disc. Once some oil drops achieve terminal velocity, the switch is closed to apply a voltage of 200 V across the discs. As a result, an oil drop of radius 8 × 10−7 m stops moving vertically and floats between the discs. The number of electrons present in this oil drop is ________. (neglect the buoyancy force, take acceleration due to gravity = 10 ms−2 and charge on an electron (e) = 1.6×10–19 C)