I have seen two approaches to the method of integration by substitution (in two different books). On searching the internet i came to know that Approach I is known as the method of integration by direct substitution whereas Approach II is known as the method of integration by indirect...
In my chemistry study material a set of rules to draw resonance structures are given. They are:
(1) Only electrons move. The nuclei of the atoms never move.
(2) The only electrons that can move are pi electrons (electrons in pi bonds) and lone-pair electrons.
(3) The total number of electrons...
1. Homework Statement :
A person aims a gun at a bird from a point at a horizontal distance of 100m. If the gun can impart a speed of 500m/s to the bullet , then above what height of the bird he should aim his gun to hit it ?
2. Homework Equations :
H_{max}=\frac{u^2\sin^2\theta}{2g}...
1. Homework Statement :
r vector = 3t i + (4t-5t2)j. Find the angle made by the vector with respect to the x-axis and the y-axis.
2. Homework Equations :
A.B=AxBx+AyBy
3. The Attempt at a Solution :
I tried to take the dot product of the unit vector along x-axis and r. I did the same for...
Doubts regarding the law of reciprocal proportions: What i have understood by reading the definition is that the ratio of the masses in which two elements A and B combine with a fixed mass of a third element C, will be a whole number multiple of the ratio of the masses in which A and B combine...
1. Homework Statement : Determine the resultant of three vectors of magnitude 1, 2 and 3 whose directions are those of sides of an equilateral triangle taken in order.
2. Homework Equations :
R2 = A2 + B2 + 2 A B cos θ
tan α = B sin θ/(A+B cos θ)
3. The Attempt at a Solution ...
Background: Amount of substance is a fundamental physical quantity which has mole (mol) as it's SI unit. Therefore all expressions for amount of substance should have the unit mole on simplification.
Therefore, if A = Amount of substance (normally in moles), m = Mass of the substance in a...
I am facing a lot of problem in proving trigonometric results (advanced ones). There are a lot of formulas (compound angle related ones, transformation of sum into product ones and vice versa, multiple angle and sub-multiple angle ones). I am unable to figure out how to proceed forward in...
1. Homework Statement
P(x) =ax2+bx+c where a, b and c are in arithmetic progression and are positive. α and β are the roots of the equation and are integers. Find the value of α+β+αβ. (Answer is 7)
2. Homework Equations
x = {−b ± √(b2 − 4ac)} /2a
3. The Attempt at a Solution
Since a, b and c...
Background: I have just started studying vector algebra. I studied that physical quantities like velocity, force, momentum, etc. are vectors (My book addresses them as polar vectors/true vectors) and physical quantities like quantities like angular velocity, torque, angular momentum are also...
I have just started studying vector algebra and i was wondering how is the direction of a vector (or any point object) specified in 3 dimensions. I know how to indicate the direction of a vector in 1 dimension and 2 dimensions. Is the direction of a vector in 3 dimensions stated by using angles...
Suppose there are two objects, denoted by A and B. When they collide with each other with the condition that A is stationary and B is in motion, B exerts an action force on A due to which A exerts a reaction force on B. Thus the net force exerted on A is FactionAB and the net force exerted on B...
My previous Chemistry teacher while teaching IUPAC nomenclature said that the double bond is always given greater priority over the triple bond and the numbering of the carbon atom chain is done in such a way that the double bond gets the lowest possible number while my present Chemistry teacher...
A current carrying conductor produces a magnetic field but what if there is an object which has the same speed as current. Will there be magnetic field by the current carrying conductor for that object?
I know that HCl is a compound whose 1 molecule is composed of 1 hydrogen and 1 chlorine atom bonded co-valently to each other, the bond being polar co-valent. It exists in gaseous state at room temperature. When HCl gas is dissolved in water, it dissociates to furnish H+ ions and thus HCl...
It seems at first sight of the first circuit that all the resistors of resistance r are connected in parallel and i have thus simplified it to the second circuit. But then on numbering the nodes and redrawing the circuit i got the third circuit.
I got the same equivalent resistance for all the...
According to Ohm's law, "Physical conditions remaining the same, the electric current flowing through a conductor is directly proportional to the potential difference across the two ends of the conductor"
I have two conceptual queries:
FIRST
When the ends of the conductor are not connected to...
https://drive.google.com/open?id=0B3IenBvKWb4PZW9rRWg4cXptT2c
I had to find the resistance of this circuit between A and B. My teacher said that since the blank wires have zero resistance, the potential difference across the ends of the blank wire is zero(according to v = ir) and thus 1,4 are...
I have seen many instances of molecular formulas of two or more compounds with a dot between two adjacent molecular formulas like CuSO4.10H20, CaCO3.MgCO3, K2SO4.Al2(SO4)3.24H20 and so on. What does the dot indicate?
I know that a vector quantity or simply a vector is a physical quantity which has a magnitude and is associated with some definite direction. According to this definition should not pressure and current be vectors since both are associated with some definite direction?In some places they are...
Do pH and pKa refer to the same concept? The same question for pOH and pKb also.
What does kWh actually mean. In have read that it is the ionic product and is the product of [H+] and [OH-] but what does it indicate. Does it have any full form?
Why do conservative forces conserve mechanical energy while non conservative forces do not?
According to me,
What makes the conservative forces path independent is that for a particular case they always act in a fixed direction irrespective of the direction of motion of the object on which they...
I am new to number theory and I heard from my friend that we can use modular arithmetic to conveniently find the unit digit of a number or the remainder obtained on dividing a number by another number such as the remainder obtained on dividing (x^y) by a. Is it possible?How can we do this?
I know that for rigid bodies only the work-energy theorem states that the net work done on the body equals the change in kinetic energy of the body since a rigid body has no internal degrees of freedom and hence no other forms of energy such as potential energy. Is there a most generalized form...
Standing within a field, should the force required to move an object in the opposite direction of the field without acceleration be equal to the force exerted by the field on it or a little more than that?
In physics, wave mechanics and vibration specifically, do the terms note, tone and mode mean the same thing or do they refer to difference things? Also what does the mode of oscillation exactly mean?
I was having a lot of trouble understanding tension force in a string. So i decided to write a sort of essay on it. Here it is:
Tension/Tension Force
1.Tension/Tension force is the electromagnetic internal force transmitted through a rope, string, cable or a wire, when pulled taut by external...
Suppose there is a beaker filled with water placed on a weighing machine. Suppose the reading is x kg. Now, if i immerse a solid block inside the beaker without touching the walls or the bottom of the beaker, will the reading given by the weighing machine increase or not?
Suppose there is a pulley(of negligible mass) and a string(of negligible mass) passes through the groove and two equal masses are attached to each end of the string. Now, if the whole arrangement is attached on a spring balance what will be the reading of the spring balance. Will it be zero?
Does the value of the potential energy of a system of objects depend on the reference point or the nature of force existing between them (attractive or repulsive)?