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 $$y = {{{x^2}} \over 2}$$. 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 p₀. The bubble now gets compressed radially in an adiabatic manner so that its radius becomes (R $$-$$ a). For a << R the magnitude of the work done in the process in given by (4$$\pi$$p₀Ra²)X, where X is a constant and $$\gamma$$ = C_p/C_v = 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 R₃ has temperature coefficient 0.0004$$^\circ$$C^-1. If the temperature of R₃ is increased by 100$$^\circ$$C, the voltage developed between S and T will be ________ volt.