What is measurement? Measurement is the process of comparing an unknown quantity with a known quantity. Or, Measurement is expressing characteristics or properties of an object in terms of number and unit. Like expressing length of a table as 1.5 meter, mass of a rice pack as 20 kg etc. Importance of measurement Standardization:- Measurement has made standardization of physical quantities in terms of predefined known quantities possible. This led to a revolution in field of science, technology, medicine, trade and commerce. In the absence of standard quantities the ways of expressing quantities were not uniform. Conficts used to arise while exchanging goods. Quantification:- Measurement helps to quantify unknown quantities. The measured values can be used for fur...

Differences between fundamental quantities and derived quantities Fundamental quantities vs derived quantities. Independent quantities vs dependent quantities. Base quantities vs derived quantities. Base quantities, fundamental quantities and independent quantities terms are used interchangeably. While Derived quantities and dependent quantities terms are used interchangeably. The differences between fundamental and derived quantities are as follows:- Fundamental quantities Derived quantities Those physical quantities which are independent of other quantities are called fundamental or independent quantities. Those physical quantities which dependen upon fundamental quantities for their expression in mathematical form are called derived or dependent quantities. ...

Physics is defined as the scientific study which is concerned with describing the interactions of energy, matter, space, and time, and it is especially interested in what fundamental mechanisms underlie every phenomenon. Applications of physics Knowledge of physics is useful in everyday situations as well as in nonscientific professions. Physics is the foundation of many important disciplines and contributes directly to others. Some applications of physics are as follows:- Engineering :- Most branches of engineering are applied physics. In architecture, physics is at the heart of structural stability, and is involved in the acoustics, heating, lighting, and cooling of buildings. Chemistry :- In chemistry knowledge of physics is required to understand the interactions of atoms and molecules. Biology :- Physics has many applications in the biological sciences. On the microscop...

Solution Given x y = y x      .....(i) x≠y      .....(ii) Let x = ky      .....(iii) where k is a constant Equation .....(i), .....(ii) and .....(iii) implies that k≠1. Inserting x = ky in equation .....(i) (ky) y = y ky Or, k y . y y = y ky Or, k y = y ky . y -y Or, k y = y ky - y Or, k y = y y(k-1) Or, k y = (y (k-1) ) y Here power of both the sides are y so. Or, k = y (k-1) Raising both sides by power of     1  k-1    we get   Or, k   1  k-1    = y y = k   1  k-1    .....(iv) So, x = ky is given by x = k (k   1  k-1    ) x = k   1  k-1   +1  ...

Exercise 3.4 Page 120 In the equation a 1 x + b 1 y = c 1 a 2 x + b 2 y = c 2 , according to Crammer’s rule, a) Write D in determinant form. D =   Om Om    Om Om Om Om    a 1    a 2          b 1    b 2       Om Om Om Om   = a 1 b 2 - a 2 b 1 Om Om    b) Write D x in determinant form. D x =   Om Om    Om Om Om Om    c 1    c 2          b 1    b 2       Om Om Om Om   = c 1 b 2 - c 2 b 1 Om Om    c) Write D y in determinant form. D y =   Om Om    Om Om Om Om    a 1    a 2          c 1    c 2  ...