DIMENSIONAL ANALYSIS

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.

The heat produced in a wire carrying an electric current depends on the current, the resistance and the time. Assuming that the dependuance is of the product of powers type, guress an eqn. between these quantites uning dimesional analysis. The dimensional formula of resistance is ML^2 A^(-2) T^(-3) and heat is a form of energy.

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.

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.

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 :

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.

A liquid drop placed on a horizontal plane has a near spherical shape (slightly flattened due to gravity). Let R be the radius of its largest horizontal section. A small disturbance causes the drop to vibrate with frequency v about its equilibrium shape. By dimensional analysis the ratio (v)/(sqrt(sigma//rho R^(3))) can be (Here sigma is surface tension, rho is density, g is acceleration due to gravity, and k is arbitrary dimensionless constant)–