Question

38. The pair of the quantities having same dimensions is
(1) Displacement, velocity
(2) Time, frequency
(3) Wavelength, focal length
(4) Force, acceleration
T
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Answer 1

The answer is (c)Wavelength, focal length

The dimensions of the quantities are expressed in terms of the seven basic quantities such as mass, time, length, etc.

Following are the definitions of the given quantities along with their dimensions:

• Displacement: It is defined as the change in position of the body. It is the distance between the final and initial positions of a body. Distance is measured as length. Dimension of displacement = M⁰L¹T⁰

• Velocity: It is defined as the rate of change of displacement per unit time. Velocity = Displacement / Time. Velocity = L / T  

        [Velocity] = M⁰L¹T⁻¹

• Time: It is fundamental unit. [Time] = M⁰L⁰T¹
• Frequency: It is the number of times an event is occurring in unit time. Frequency = 1/ Time

       [Frequency] = M⁰L⁰T⁻¹

• Wavelength: It is the length of one wave. [Wavelength] = M⁰L¹T⁰
• Focal Length: It is the length from the center of a mirror or lens to a point from which the reflected or refracted rays converge or diverge.

        [Focal length] = M⁰L¹T⁰

• Force: It is given as the product of mass and acceleration. Acceleration is the change in velocity per unit of time.

        Force= Mass x Acceleration

        Force = M x $\frac{Velocity}{Time}$                  Force = MT⁻¹ x LT⁻¹

        [ Force ] = M¹L¹T⁻²

• Acceleration: It is given as the change in velocity per unit time.

       Acceleration = velocity / Time

       [Acceleration] = (L¹T⁻¹)/ T

       [Acceleration] = M⁰L¹T⁻²

Therefore, we can see that the dimensions of wavelength and focal length are the same.                        

Answer 2

Answer:

Answer is option three

Explanation:

We know that the dimension of these both quantities is [L]