Dimensional Analysis

Statement-I: Dimensional analysis can give us the numerical value of proportionality constants that may appear in an algebraic expression. Statement-II: Dimensional analysis make use of the fact that dimensions can be treated as algebraic quantities.

Assertion: The given equation x = x_(0) + u_(0)t + (1)/(2) at^(2) is dimensionsally correct, where x is the distance travelled by a particle in time t , initial position x_(0) initial velocity u_(0) and uniform acceleration a is along the direction of motion. Reason: Dimensional analysis can be used for cheking the dimensional consistency or homogenetly of the equation.

Expermients show that frequency (n) of a tuning fork depends on lentght (I) fo the prong, density (d) and the Young's modulus (Y) of its meterial. On the basis of dimensional analysis, dericve an expression for frequency of tunnig fork.

A : If displacement y of a particle executing simple harmonic motion depends upon amplitude a angular frequency omega and time t then the relation y=asinomegat cannot be dimensionally achieved. R : An equation cannot be achieved by dimensional analysis, if it contains dimensionless expressions.

While solving a physics problem you perform a series of algebraic manipulations that lead to a mathematical expression for distance. If F = Force, a = acceleration, v = velocity, m = mass, t = time, and N = normal force, use dimensional analysis to find which of the following expressions could be INCORRECT for distance.

A student forgot Newton's formula for speed of sound but the knows there speed (v), pressure (p) and density (d) in the formula. He then start using dimensional analysis method to find the actual relation. upsilon = kp^(x)d^(y) Where k is a dimensionless constant. On the basis of above passage answer the following questions: The value of y is :

A student forgot Newton's formula for speed of sound but the knows there speed (v), pressure (p) and density (d) in the formula. He then start using dimensional analysis method to find the actual relation. upsilon = kp^(x)d^(y) Where k is a dimensionless constant. On the basis of above passage answer the following questions: The value of x is :

A particle with mass m and initial speed V_(0) is a subject to a velocity-dependent damping force of the form bV^(n) .With dimensional analysis determine how the stopping time depends on m, V_(0) and b for begin with writing Deltat=Am^(alpha)b^(beta)V_(0)^(gamma) , powers alpha, beta and gamma will be.

A student forgot Newton's formula for speed of sound but the knows there speed (v), pressure (p) and density (d) in the formula. He then start using dimensional analysis method to find the actual relation. upsilon = kp^(x)d^(y) Where k is a dimensionless constant. On the basis of above passage answer the following questions: If the density will increase the speed of sound will :