An unknown, quantity X multiplied by velocity is equal to power. Identify X, by dimensional analysis.

Establish an expression for critical velocity from the method of dimensional analysis.

Four different expressions for displacement of a particle executing simple harmonic motion are printed on a book: Here a = maximum displacement of the particle , v =its velocity and T = its time period. Check from dimensional analysis which of these expressions involve (s) some printing mistake.

Identify 'X' in the figure.

If two physical quantities a and b are related by the equation a= kb where k is dimensionless constant, then the principle of dimensional homogeneity demands that a and b have the same dimension. However the proportionality constant k cannot be determined by dimensional analysis only. It may at most be written that a prop b if a and b are of the same dimension. A coil of inductance L stores an amount of energy (1)/(2)Ll^(2) when a current I passes through it. The dimension of L is

It two physical quantities a and b are related by the equation a= kb where k is dimensionless constant, then the principle of dimensional homogeneity demands that a and b have the same dimension. However the proportionality constant k cannot be determined by dimensional analysis only. It may at most be written that a prop b if a and b are of the same dimension. If a particle of mass m executes simple harmonic motion with amplitude A and frequency f, then its energy is proportional to

It two physical quantities a and b are related by the equation a = kb where k is dimensionless constant, then the principle of dimensional homogeneity demands that a and b have the same dimension. However the proportionality constant k cannot be determined by dimensional analysis only. It may at most be written that a prop b if a and b are of the same dimension. Time period (T) of oscillation of a liquid drop depends on its radius r the density rho and the surface tension sigma of the liquid. Then T is proportional to

The wave velocity (v) inside water depends on the wavelength (lambda) of the wave the density ( sigma ) of water and acceleration due to gravity (g). Work out the relation among the quantities from dimensional analysis.

An atom of X contains 17 protons ad 18 neutrons. Identify X.

The velocity (v ) of sound in a gas depends on the pressure (p) and density ( sigma ) of the gas. Using dimensional analysis establish a relation between v,p and sigma .

Solve 3x-6=0 graphically in two dimensional plane.