Definition Acceleration of an object is defined as the time rate of change of velocity of an object. Introduction We often see that the velocity of a vehicle moving on road is never uniform. Its a velocity that changes randomly. Such a motion is called an accelerated motion. Thus, acceleration is the change in velocity […]
The acceleration due to gravity of earth is the rate of increase of velocity of a body falling freely towards the earth. It is denoted by ‘g’.
Consider the earth is a perfect sphere of mass 'M' and radius 'R' and whole mass of the earth is supposed to be concentrated at the centre 'O'. Let a body of mass 'm' is lying on the surface of earth....
Apparent weight of a today is the weight which does not actually exist. But it appears when the body is kept in a lift or elevator.
We know that earth attracts everybody towards its centre with some force of attraction called Gravity force. Due to this force of gravity, all the bodies experience their weight. If ‘m’ is the mass of a body then its weight is ‘mg’ (vertically downwards) which is equal to the gravity force....
Basic forces in nature are the forces governing macroscopic as well as microscopic world. These are gravitation forces, weak forces, electromagnetic forces and nuclear forces.
In daily life, we come across many kinds of forces like friction forces, electrostatic forces, magnetic forces, viscous forces etc. These forces are observed to be acting between macroscopic objects. For instance, while walking on rough horizontal surface, the frictional forces....
The energy required to remove a satellite from its orbit around the earth to infinity is called Binding energy of a satellite.
We know that the satellite revolves around the earth in an orbit near the surface of earth. The satellite gets the necessary centripetal force from the gravitational force of earth. Assume a satellite, revolving around the earth of mass 'Me' and radius 'Re'. It is height 'h' above the surface of earth. If 'v' is the orbital velocity of the satellite and 'm' is the mass....
Step 1 : Invert the number
If z = a + i b is a complex number, then reciprocal of it is given by..
Step 2: Multiply numerator and denominator by conjugate
Multiply numerator and denominator of the inverted number by conjugate of denominator...
Step 3: Simplify and find the reciprocal
Simplify above equation in step (2). Numerator is multiplied by 1 and is already simplified...
Argand Plane is used to represent the complex number. The horizontal axis of Argand plane represents the real part while vertical axis represents the imaginary part of complex number.
The modulus of complex number is distance of a point P (which represents complex number in Argand Plane) from the origin....
Let a + i b be a complex number whose logarithm is to be found.
Step 1: Convert the given complex number, into polar form.
Where amplitude and argument is given.
Step 2: Use Euler’s Theorem to rewrite complex number in polar form to exponential form.
There r (cos θ + isinθ) is written as reiθ. This means that
a+ i b= reiθ
Step 3: Take logarithm of both sides we get.
The complex number z in geometrical form is written as z = x + iy.In geometrical representation complex number z is represented by a point P(x, y) on the complex plane or the argand plane where OA =x is x-intecept and AP=y is y-intercept.
In polar representation a complex number z is represented by two parameters ‘r’ and ‘θ’. Parameter ‘r’ is the modulus of complex number and parameter ‘θ’ is the angle which the line OP makes with the positive direction of x-axis. It is also called argument of complex number and is denoted by arg(z).Finding the value of these two parameters from parameters x and y will help us convert the complex number to polar form.