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Two identical non-conducting solid spheres of same mass and charge are suspended in the air from a common point by two non-conducting, massless strings of the same length. At equilibrium, the angle between the strings is α. 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

a) electric force between the spheres remains unchanged b) electric force between the spheres reduces c) mass density of the spheres is 840 kg... View Article

In an X-ray tube, electrons emitted from a filament (cathode) carrying current I hit a target (anode) at a distance d from the cathode. The target is kept at a potential V higher than the cathode resulting in the emission of continuous and characteristic X-rays. If the filament current is decreased to 1/2, the d potential difference Vis increased to 2v, and the separation distance d is reduced to d/2, then

a) the cut-off wavelength will reduce to half, and the wavelengths of the characteristic X-rays will remain the same b) the cut-off wavelength,... View Article

A student skates up a ramp that makes an angle 30° with the horizontal. He/she starts (as shown in the figure) at the bottom of the ramp with speed 0 and wants to turn around over a semi-circular path xyz of radius R during which he/she reaches a maximum height h (at point y) from the ground as shown in the figure. Assume that the energy loss is negligible and the force required for this turn at the highest point is provided by his/her weight only. Then (g is the acceleration due to gravity)

a) v02 - 2gh = (1/2) gR b) v02 - 2gh = (√3/2) gR c) the centripetal force required at points x and z is zero d) the centripetal force... View Article

A beaker of radius r is filled with water (refractive index 4/3) up to a height H as shown in the figure on the left. The beaker is kept on a horizontal table rotating with angular speed & omega;. This makes the water surface curved so that the difference in the height of water level at the centre and at the circumference of the beaker is h(h <<H, h << r), as shown in the figure on the right. Take this surface to be approximately spherical with a radius of curvature R. Which of the following is/are correct? (g is the acceleration due to gravity)

a) R = b) R = c) Apparent depth of the bottom of the beaker is close to d) Apparent depth of the bottom of the beaker is close to... View Article