Question

 

When a wave traverses a medium, the displacement of a particle located atx at time t is given by 

                            

Where ab and c are constants of the wave. Which of the following are dimensionless quantities?

Solution

Correct option is

y/a, bt and cx

Since the sine function in dimensionless, sin (bt – cx) is dimensionless. Therefore, y and a must have the same dimensions, i.e. y/a is dimensionless. Since the argument of a sine function (or any trigonometric function) must be dimensionless, bt and cx are also dimensionless.

SIMILAR QUESTIONS

Q1

 

According to the quantum theory, the energy E of a photon of frequency v is given by 

                               

Where h is Plank’s constant. What is the dimensional formula for h?

Q2

What is the SI unit of Plank’s constant?

Q3

 

The volume V of water passing any point of a uniform tube during tseconds is related to the cross-sectional area A of the tube and velocity uof water by the relation  

                                   

Which one of the following will be true?

Q4

Which one of the following relations is dimensionally consistent where h is height to which a liquid of density ρ rises in a capillary tube of radius, rTis the surface tension of the liquid, θ the angle of contact and g the acceleration due to gravity?

Q5

 

The frequency n of vibrations of uniform string of length l and stretched with a force F is given by

                              

Where p is the number of segments of the vibrating string and m is a constant of the string. What are the dimensions of m?

Q6

What is the relationship between dyne and Newton of force?

Q7

 

The Vander Waal equation for n moles of a real gas is 

                              

Where P is the pressure, V is the volume, T is the absolute temperature, R is the molar gas constant and ab are Vander Waal constants. The dimensions of a are the same as those of

Q8

In velocity (V), acceleration (A) and force (F) are taken as fundamental quantities instead of mass (M), length (L) and time (T), the dimensions of Young’s modulus would be

Q9

The dimensions of permittivity (ε0) of vacuum are