The height of victoria falls is 63 m. What is the difference in temperature of water at the top and at the bottom of fall? [Given 1 cal = 4.2 J and specific heat of water = 1 cal g$$-$$1 $${}^{\circ }$$0C$$-$$1]

A reversible engine has an efficiency of {1 \over 4}. If the temperature of the sink is reduced by 58$${}^{\circ }$$C, its efficiency becomes double. Calculate the temperature of the sink :

For an ideal gas the instantaneous change in pressure 'p' with volume 'v' is given by the equation {{dp} \over {dv}} = - ap. If p = p0 at v =0 is the given boundary condition, then the maximum temperature one mole of gas can attain is : (Here R is the gas constant)

Two thin metallic spherical shells of radii r1 and r2 (r1 < r2) are placed with their centres coinciding. A material of thermal conductivity K is filled in the space between the shells. The inner shell is maintained at temperature $$\theta$$1 and the outer shell at temperature $$\theta$$2($$\theta$$1 < $$\theta$$2). The rate at which heat flows radially through the material is :-

A mixture of hydrogen and oxygen has volume 500 cm3, temperature 300 K, pressure 400 kPa and mass 0.76 g. The ratio of masses of oxygen to hydrogen will be :-

A cube of side 'a' has point charges +Q located at each of its vertices except at the origin where the charge is $$-$$Q. The electric field at the centre of cube is :

Two electrons each are fixed at a distance '2d'. A third charge proton placed at the midpoint is displaced slightly by a distance x (x << d) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency : (m = mass of charged particle)

A charge 'q' is placed at one corner of a cube as shown in figure. The flux of electrostatic field $$\overrightarrow{E}$$ through the shaded area is :

Find the electric field at point P (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length L carrying a charge Q. The distance of the point P from the centre of the rod is a = {{\sqrt 3 } \over 2}L.

Given below are two statements: Statement I : An electric dipole is placed at the center of a hollow sphere. The flux of the electric field through the sphere is zero but the electric field is not zero anywhere in the sphere. Statement II : If R is the radius of a solid metallic sphere and Q be the total charge on it. The electric field at any point on the spherical surface of radius r (

An inclined plane making an angle of 30$${}^{\circ }$$ with the horizontal is placed in a uniform horizontal electric field 200{N \over C} as shown in the figure. A body of mass 1 kg and charge 5 mC is allowed to slide down from rest at a height of 1 m. If the coefficient of friction is 0.2, find the time taken by the body to reach the bottom. [g = 9.8 m/s2; \sin 30^\circ = {1 \over 2}; \cos 30^\circ = {{\sqrt 3 } \over 2}]

Find out the surface charge density at the intersection of point x = 3 m plane and x-axis, in the region of uniform line charge of 8 nC/m lying along the z-axis in free space.

An oil drop of radius 2 mm with a density 3g cm$$-$$3 is held stationary under a constant electric field 3.55 $$\times$$ 105 V m$$-$$1 in the Millikan's oil drop experiment. What is the number of excess electrons that the oil drop will possess? (consider g = 9.81 m/s2)

A certain charge Q is divided into two parts q and (Q $$-$$ q). How should the charges Q and q be divided so that q and (Q $$-$$ q) placed at a certain distance apart experience maximum electrostatic repulsion?

An electric dipole is placed on x-axis in proximity to a line charge of linear charge density 3.0 $$\times$$ 10$$-$$6 C/m. Line charge is placed on z-axis and positive and negative charge of dipole is at a distance of 10 mm and 12 mm from the origin respectively. If total force of 4N is exerted on the dipole, find out the amount of positive or negative charge of the dipole.

Two ideal electric dipoles A and B, having their dipole moment p1 and p2 respectively are placed on a plane with their centres at O as shown in the figure. At point C on the axis of dipole A, the resultant electric field is making an angle of 37$${}^{\circ }$$ with the axis. The ratio of the dipole moment of A and B, {{{p_1}} \over {{p_2}}} is : (take \sin 37^\circ = {3 \over 5})

Two identical tennis balls each having mass 'm' and charge 'q' are suspended from a fixed point by threads of length 'l'. What is the equilibrium separation when each thread makes a small angle '$$\theta$$' with the vertical?

What will be the magnitude of electric field at point O as shown in the figure? Each side of the figure is l and perpendicular to each other?

A solid metal sphere of radius R having charge q is enclosed inside the concentric spherical shell of inner radius a and outer radius b as shown in the figure. The approximate variation electric field $$\overrightarrow{E}$$ as a function of distance r from centre O is given by

The two thin coaxial rings, each of radius 'a' and having charges +Q and $$-$$Q respectively are separated by a distance of 's'. The potential difference between the centres of the two rings is :