When a wave traverses a medium, the displacement of a particle located atx at time t is given by
Where a, b and c are constants of the wave. Which of the following are dimensionless quantities?
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.
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?
What is the SI unit of Plank’s constant?
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?
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, r, Tis the surface tension of the liquid, θ the angle of contact and g the acceleration due to gravity?
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?
What is the relationship between dyne and Newton of force?
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 a, b are Vander Waal constants. The dimensions of a are the same as those of
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
The dimensions of permittivity (ε0) of vacuum are