A : All physically correct equations are dimensionally correct.
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Can a dimensionally correct equation be incorrect?
Solution : A dimensionally correct equation may or may not be correct. For example , ` s = ut + at^(2)` is dimensionally correct , but not correct actually.
A dimensionally incorrect equation may be correct also . For example , `s = u + ( a)/( 2) ( 2n -1)` is a correct equation , but not correct dimensionally.
What is physically correct equation?
To check the correctness of physical equation, v = u + at, Where ‘u’ is the initial velocity, ‘v’ is the final velocity, ‘a’ is the acceleration and ‘t’ is the time in which the change occurs.
Does dimensional consistency ensure the physical correctness of a mathematical equation?
Dimensions are customarily used as a preliminary test of the consistency of an equation, when there is some doubt about the correctness of the equation. However, the dimensional consistency does not guarantee correct equations. It is uncertain to the extent of dimensionless quantities or functions.
What does dimensionally correct mean?
Dimensionally Correct In an algebraic expression, all terms which are added or subtracted must have the same dimensions. This implies that each term on the left-hand side of an equation must have the same dimensions as each term on the right-hand side.
Can a dimensional analysis tell you that a physical relation is completely right explain with an example?
No, dimensional analysis does not tell that a physical relation is completely right because numerical factors in the relation cannot be determined.
Are all dimensionally correct equation numerically correct?
Answer: โโ โ No all dimensionally correct equations are not numerically correct because in the use of dimensions numerical constants are said to be dimensionless and thus we cannot specify if there is the need of numerical constants in the equations.
Which one is not a dimensional number?
The correct answer is Angle.
Which of the following is incorrect all derived quantities?
The dimension of a derived quantity is never zero in any base quantity. This statement is incorrect because derived quantities may have zero dimensions in certain base quantities. For example, acceleration, which is a derived quantity, has zero dimensions in the mass, which is a base quantity.
Which of the following relations is dimensionally incorrect *?
$ u^2 = 2a(gt – 1) $ where $ g $ must be the acceleration due to gravity. Now, from the first principle stated above, option C must be dimensionally incorrect because it has the subtraction of dimensionless constant with a quantity with dimension. Hence, the correct option is option C.
What are the limitations of dimensional analysis?
The limitations of dimensional analysis are: (i) We cannot derive the formulae involving trigonometric functions, exponential functions, log functions etc., which have no dimension. (ii) It does not give us any information about the dimensional constants in the formula.
How do you show that an equation is dimensionally consistent?
The only way in which this can be the case is if all laws of physics are dimensionally consistent: i.e., the quantities on the left- and right-hand sides of the equality sign in any given law of physics must have the same dimensions (i.e., the same combinations of length, mass, and time).
Which relation Cannot be obtained dimensionally?
(A): Physical relations involving addition and subtraction cannot be derived by dimensional analysis.
Can we use dimensional method to find an expression?
can we use the dimensional method to find an expression for gravitational force acting between two objects of mass m1 and m2. Help experts. No, we can not use dimension analysis to find out the gravitational force between the two masses because gravitational constant(G) is the dimensional quantity.
What is the dimensional formula of electron volt?
Electronvolt (eV) has a dimension of ML2T-2 where M is mass, L is length, and T is time. It can be converted to the corresponding standard SI unit J by multiplying its value by a factor of 1.60217733E-019.
Which formula is dimensionally correct?
Therefore the equation is dimensionally correct. The angle subtended by an arc of length l, circle of radius r, at the center is given by t/r. Thus, we can say that formula ฮธ = r/l is dimensionally correct but numerically wrong.
What are dimensions of physical quantities?
There are five fundamental dimensions in terms of which the dimensions of all other physical quantities may be expressed. They are mass [M], length [L], time [T], temperature [ฮธ], and charge.
How do you find the dimensions of physical quantities?
How do you derive the relationship between physical quantities?
Finding relations between physical quantities in a physical phenomenon. The principle of Homogeneity can be used to derive the relations between various physical quantities in a physical phenomenon.
How do you check the correctness of an equation in physics?
How do you test the correctness of dimensional analysis?
Solution : Dimension for distances s = [L]
Dimension or initial velocity u = `[LT^(-1)]`
Dimension for time t = [T]
Dimension for acceleration a = `[LT^(-2)]`
According to the principle of homogeneity,
Dimensions of LHS = Dimensions of RHS
Substituting the dimensions in the given formula < ...
What is the dimensional formula for torque?
Therefore, the torque is dimensionally represented as [M L2 T-2].
Which of the following is not dimensionless physical quantity?
This means that angular momentum is not a dimensionless quantity. Therefore, no given quantities are dimensionless. So, the correct answer is “Option D”.
Which of the following is a dimensionless physical quantity?
Stress is ratio of same physical quantities hence dimensionless. Answer: Strain is ratio of two lengths , a measure of deformation – increase/decrease in length wrt original length. Thus its dimensionless , option B is correct.
How many supplementary physical quantities are there?
Supplementary : Beside the seven fundamental physical quantities two supplementary quantities are also defined, they are : (1) Plane angle (2) Solid angle. MAGNITUDE : Magnitude of physical quantity = (numerical value) ร (unit) Magnitude of a physical quantity is always constant.