Which Principle Is Used To Check The Dimensional Correctness Of An Equation?

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The time period of a simple pendulum is given by T=2π√lg, where l is length of the pendulum and g is acceleration due to gravity. Show that this equation is dimensionally correct. … In the above equation, the dimensions of both the LHS and the RHS are the same. This means that the given equation is dimensionally correct.

How can we check the dimensional correctness explain it with example?

Example 1: Check the correctness of physical equation s = ut + ½ at2. In the equation, s is the displacement, u is the initial velocity, v is the final velocity, a is the acceleration and t is the time in which change occurs. Hence, by the principle of homogeneity, the given equation is dimensionally correct.

What is the dimension of T 2π √ m k?

dimension of k? Verify the dimensional correctness of the formula t = 2π √m k for the period of oscillation of a mass m suspended by a spring of stiffness k. Answer Since T is a force, it has dimensions of −2.

What is dimensional formula?

Dimensional formula (equation) (Definition) : An equation, which gives the relation between fundamental units and derived units in terms of dimensions is called dimensional formula (equation). In mechanics the length, mass and time are taken as three base dimensions and are represented by letters L, M, T respectively.

What is the formula of time period?

The formula for the period T of a pendulum is T = 2π Square root of√L/g, where L is the length of the pendulum and g is the acceleration due to gravity.

Which equation of motion 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 is dimensional correctness?

Here the dimensions of every term in the given physical relation are the same, hence the given physical relation is dimensionally correct.

What is a dimensional check?

The dimensional checks are carried out to check the geometrical and dimensional regularity of the article. Such tests are often necessary to test the repeatability of the machined articles, especially in the automotive field. Various types of dimensional checks belong to this category.

Why is T 2π √ l g?

Pendulum – Where a mass m attached to the end of a pendulum of length l, will oscillate with a period (T). Described by: T = 2π√(l/g), where g is the gravitational acceleration. … By timing the duration of one complete oscillation we can determine the period and hence the frequency.

What is T 2pi sqrt l g?

The period of a simple pendulum is T=2π√Lg T = 2 π L g , where L is the length of the string and g is the acceleration due to gravity.

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What is V 2πr T?

v=T2πr​ In Physics, Uniform Circular Motion is used to describe the motion of an object traveling at a constant speed in a circle. … Here, r represents the radius of the circle, T the time it takes for the object to make one complete revolution, called a period.

What are dimensional constants?

Gravitational constant. Hint: The physical quantities which have dimensions and have a fixed value are called dimensional constant.

What is the formula of homogeneity?

Test the dimensional homogeneity of the following equation: h = h0 + v0t + 1/2gt^2.

What is the basis of the principle of H * * * * * * * * * * of dimensions?

The principle of homogeneity states that the dimensions of each the terms of a dimensional equation on both sides are the same. Using this principle, the given equation will have the same dimension on both sides. Since All are of Dimension L , the result of sum is also equal to L.

What is the dimensional formula of H?

ML−2T−2.

What is the dimensional formula of final velocity?

Derivation. Therefore, velocity is dimensionally represented as .

What is the dimensional formula of E mc2?

Or, E = × 2 = M1 L2 T2. Therefore, energy is dimensionally represented as M1 L2 T2.

What is the dimensionally wrong equation?

A dimensionally correct equations need not be necessarily correct physical relation. A dimensionally wrong equation is not correct mathematically too.

Can an equation be dimensionally incorrect?

A dimensionally correct equation may or may not be correct. For example , s=ut+at2 is dimensionally correct , but not correct actually. A dimensionally incorrect equation may be correct also . For example , s=u+a2(2n-1) is a correct equation , but not correct dimensionally.

Can a dimensionally incorrect equation be true?

A dimensionally incorrect equation must be not incorrect.

What is the period wave?

Wave Period: The time it takes for two successive crests (one wavelength) to pass a specified point. The wave period is often referenced in seconds, e.g. one wave every 6 seconds. Fetch: The uninterrupted area or distance over which the wind blows (in the same direction).

What is T in SHM?

The maximum x-position (A) is called the amplitude of the motion. The block begins to oscillate in SHM between x=+A and x=−A, where A is the amplitude of the motion and T is the period of the oscillation. The period is the time for one oscillation.

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