JEE (Advanced) 2020 Paper-2

Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings is $$\alpha$$. The spheres are now immersed in a dielectric liquid of density 800 kg m$$^{−3}$$ and dielectric constant 21. If the angle between the strings remains the same after the immersion, then

Starting at time 𝑡=0 from the origin with speed 1 ms$$^{-1}$$, a particle follows a two-dimensional trajectory in the x-y plane so that its coordinates are related by the equation $$y = \frac{x^2}{2}$$. The x and y components of its acceleration are denoted by $$𝑎_𝑥$$ and $$𝑎_y$$, respectively. Then

A spherical bubble inside water has radius 𝑅. Take the pressure inside the bubble and the water pressure to be $$p_0$$. The bubble now gets compressed radially in an adiabatic manner so that its radius becomes (𝑅 − 𝑎). For $$a \ll R$$ the magnitude of the work done in the process is given by $$(4 \pi p_0 R a^2)X^2$$, where 𝑋 is a constant and $$\gamma = \frac{C_p}{C_V} = \frac{41}{30}$$. The value of X is ____________.

In the balanced condition, the values of the resistances of the four arms of a Wheatstone bridge are shown in the figure below. The resistance $$𝑅_3$$ has temperature coefficient 0.0004 $$^\circ C^{−1}$$. If the temperature of $$𝑅_3$$ is increased by 100 $$^\circ C$$, the voltage developed between 𝑆 and 𝑇 will be __________ volt.

Two capacitors with capacitance values $$C_1 = 2000 \pm 10$$ pF and $$C_2 = 3000 \pm 15$$ pF are connected in series. The voltage applied across this combination is $$𝑉 = 5.00 \pm 0.02$$ V. The percentage error in the calculation of the energy stored in this combination of capacitors is _______.

A cubical solid aluminium (bulk modulus = $$-V \frac{dP}{dV} = 70$$ GPa) block has an edge length of 1 m on the surface of the earth. It is kept on the floor of a 5 km deep ocean. Taking the average density of water and the acceleration due to gravity to be 10$$^3$$ kg m$$^{−3}$$ and 10 ms$$^{−2}$$, respectively, the change in the edge length of the block in mm is _____.

The inductors of two 𝐿𝑅 circuits are placed next to each other, as shown in the figure. The values of the self-inductance of the inductors, resistances, mutual-inductance and applied voltages are specified in the given circuit. After both the switches are closed simultaneously, the total work done by the batteries against the induced 𝐸𝑀𝐹 in the inductors by the time the currents reach their steady state values is________ mJ.

A container with 1 kg of water in it is kept in sunlight, which causes the water to get warmer than the surroundings. The average energy per unit time per unit area received due to the sunlight is 700 Wm$$^{−2}$$ and it is absorbed by the water over an effective area of 0.05 m$$^2$$. Assuming that the heat loss from the water to the surroundings is governed by Newton’s law of cooling, the difference (in $$^\circ C$$) in the temperature of water and the surroundings after a long time will be _____________. (Ignore effect of the container, and take constant for Newton’s law of cooling = 0.001 s$$^{−1}$$, Heat capacity of water = 4200 J kg$$^{−1}$$ K$$^{−1}$$)

The $$1^{st}, 2^{nd}$$ and the $$3^{rd}$$ ionization enthalpies, $$I_1, I_2$$ and $$I_3$$, of four atoms with atomic numbers 𝑛, 𝑛 + 1, 𝑛 + 2, and 𝑛 + 3 , where 𝑛 < 10, are tabulated below. What is the value of 𝑛?

Consider the following compounds in the liquid form:
$$O_2, HF, H_2O, NH_3, H_2O_2, CCl_4, CHCl_3, C_6H_6, C_6H_5Cl$$.
When a charged comb is brought near their flowing stream, how many of them show deflection as per the following figure?