A uniform capillary tube of inner radius $$r$$ is dipped vertically into a beaker filled with water. The water rises to a height $$h$$ in the capillary tube above the water surface in the beaker. The surface tension of water is $$\sigma .$$ The angle of contact between water and the wall of the capillary tube is $$\theta .$$ Ignore the mass of water in the meniscus. Which of the following statements is (are) true?

Two infinitely long straight wires lie in the $$xy$$-plane along the lines $$x = \pm R.$$ The wire located at $$x = + R$$ carries a constant current $${I_1}$$ and the wire located at $$x=-R$$ carries a constant current $${I_2}.$$ A circular loop of radius $$R$$ is suspended with its center at $$\left( {0,0,\sqrt 3 R} \right)$$ and in a plane parallel to the $$xy$$-plane. This loop carries a constant current $$I$$ in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the $$ + \widehat j$$ direction. which of the following statements regarding the magnetic field $$\overrightarrow B $$ is (are) true?

Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed $$1.0\,m{s^{ - 1}}$$ and the man behind walks at a speed $$2.0\,m{s^{ - 1}}.$$ A third man in standing at a height $$12$$ $$m$$ above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which emit a sound of frequency $$1430$$ $$Hz$$. The speed of sound in air is $$330\,m{s^{ - 1}}.$$ At the instant, when the moving men are $$10$$ $$m$$ apart, the stationary man is equidistant from them. The frequency of beats in $$Hz,$$ heard by the stationary man at this instant, is _____________.

A spring-block system is resting on a frictionless floor as shown in the figure. The spring constant is $$2.0\,N{m^{ - 1}}$$ and the mass of the block is $$2.0$$ $$kg.$$ Ignore the mass of the spring. Initially the spring is an unstretched condition. Another block of mass $$1.0$$ $$kg$$ moving with a speed of $$2.0$$ $$m{s^{ - 1}}$$ collides elastically with the first block. The collision is such that the $$2.0$$ $$kg$$ block does not hit the wall. The distance, in metres, between the two blocks when the spring returns to its unstretched position for the first time after the collision is __________.