Physics

If qf is the free charge on the capacitor plates and qb is the bound charge on the dielectric slab of dielectric constant k placed between the capacitor plates, then bound charge qb can be expressed as:

Two ions having same mass have charges in the ratio 1 : 2. They are projected normally in a uniform magnetic field with their speeds in the ratio 2 : 3. The ratio of the radii of their circular trajectories is :

A force F = (40î + 10?)N acts on a body of mass 5 kg. If the body starts from rest, its position vector r at time t = 10s, will be :

Consider a planet in some solar system which has a mass double the mass of earth and density equal to the average density of earth. If the weight of an object on earth is W, the weight of the same object on that planet will be :

A prism of refractive index μ and angle of prism A is placed in the position of minimum angle of deviation. If minimum angle of deviation is also A, then in terms of refractive index value of A is :

Two billiard balls of equal mass 30g strike a rigid wall with same speed of 108 kmph (as shown) but at different angles. If the balls get reflected with the same speed then the ratio of the magnitude of impulses imparted to ball 'a' and ball 'b' by the wall along 'X' direction is :
(Diagram shows ball 'a' hitting the wall perpendicularly along the x-axis and ball 'b' hitting the wall at a 45° angle to the x-axis.)

The relation between time t and distance x for a moving body is given as t = mx² + nx, where m and n are constants. The retardation of the motion is: (Where v stands for velocity)

A 10 Ω resistance is connected across 220 V - 50Hz AC supply. The time taken by the current to change from its maximum value to the rms value is :

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° with the axis. The ratio of the dipole moment of A and B, p₁ and p₂ , is:
(take sin 37° = 3/5)

Two vectors X and Y have equal magnitude. The magnitude of (X - Y) is n times the magnitude of (X + Y). The angle between X and Y is :