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A dimensionally wrong equation in which ...

A dimensionally wrong equation in which principle of homogenity of dimensions is violated must be wrong. Can you say that, a dimensionally correct question should always be right?

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Using the principle of homogeneity of dimensions, which of the following is correct?

Assertion: A dimensionally wrong or inconsistaent equation must be wrong. Reason: A dimensionally consistent equation is a exact or a correct equation.

(A) The correctness of an equation is verified using the principle of homogeneity (B) All unit less quantities are dimensional less.

From the dimensional consideration, which of the following equation is correct

A circular railway track of radius r is banked at angle theta so that a train moving with speed v can safely go round the track. A student writes: tan theta =rg//v^(2) . Why this relation is not correct? (i) Equality of dimensions does not guarantee correctness of the relation . (ii) Dimensionally correct relation may not be numerically correct. iii) The relation is dimensionally incorrect.

Choose the correct statement(s) from the given statements (I) The proportionality constant in an equation can be obtained by dimensional analysis. (II) The equation V = u + at can be derived by dimensional method. (III) The equation y = A sin omega t cannot be derived by dimensional method (IV) The equation eta = (A)/(B)e^(-Bt) can be derived with dimensional method

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 physical quantity is a phyical property of a phenomenon , body, or substance , that can be quantified by measurement. The magnitude of the components of a vector are to be considered dimensionally distinct. For example , rather than an undifferentiated length unit L, we may represent length in the x direction as L_(x) , and so forth. This requirement status ultimately from the requirement that each component of a physically meaningful equation (scaler or vector) must be dimensionally consistent . As as example , suppose we wish to calculate the drift S of a swimmer crossing a river flowing with velocity V_(x) and of widht D and he is swimming in direction perpendicular to the river flow with velocity V_(y) relation to river, assuming no use of directed lengths, the quantities of interest are then V_(x),V_(y) both dimensioned as (L)/(T) , S the drift and D width of river both having dimension L. with these four quantities, we may conclude tha the equation for the drift S may be written : S prop V_(x)^(a)V_(y)^(b)D^(c) Or dimensionally L=((L)/(T))^(a+b)xx(L)^(c) from which we may deduce that a+b+c=1 and a+b=0, which leaves one of these exponents undetermined. If, however, we use directed length dimensions, then V_(x) will be dimensioned as (L_(x))/(T), V_(y) as (L_(y))/(T), S as L_(x)" and " D as L_(y) . The dimensional equation becomes : L_(x)=((L_(x))/(T))^(a) ((L_(y))/(T))^(b)(L_(y))^(c) and we may solve completely as a=1,b=-1 and c=1. The increase in deductive power gained by the use of directed length dimensions is apparent. A conveyer belt of width D is moving along x-axis with velocity V. A man moving with velocity U on the belt in the direction perpedicular to the belt's velocity with respect to belt want to cross the belt. The correct expression for the drift (S) suffered by man is given by (k is numerical costant )

A physical quantity is a phyical property of a phenomenon , body, or substance , that can be quantified by measurement. The magnitude of the components of a vector are to be considered dimensionally distinct. For example , rather than an undifferentiated length unit L, we may represent length in the x direction as L_(x) , and so forth. This requirement status ultimately from the requirement that each component of a physically meaningful equation (scaler or vector) must be dimensionally consistent . As as example , suppose we wish to calculate the drift S of a swimmer crossing a river flowing with velocity V_(x) and of widht D and he is swimming in direction perpendicular to the river flow with velocity V_(y) relation to river, assuming no use of directed lengths, the quantities of interest are then V_(x),V_(y) both dimensioned as (L)/(T) , S the drift and D width of river both having dimension L. with these four quantities, we may conclude tha the equation for the drift S may be written : S prop V_(x)^(a)V_(y)^(b)D^(c) Or dimensionally L=((L)/(T))^(a+b)xx(L)^(c) from which we may deduce that a+b+c=1 and a+b=0, which leaves one of these exponents undetermined. If, however, we use directed length dimensions, then V_(x) will be dimensioned as (L_(x))/(T), V_(y) as (L_(y))/(T) , S as L_(x)" and " D as L_(y) . The dimensional equation becomes : L_(x)=((L_(x))/(T))^(a) ((L_(y))/(T))^(b)(L_(y))^(c) and we may solve completely as a=1,b=-1 and c=1. The increase in deductive power gained by the use of directed length dimensions is apparent. Which of the following is not a physical quantity

These questions consists of two statements each printed as Assertion and Reason. While answering these question you are required to choose any one of the following five reponses (a) If both Assertion and Reason arecorrect and Reason is the correct explanation of Asserrtion. (b) If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion. (c ) If Assertion is true but Reason is false. (d) If Assertion is false but Reason is true. Assertion Force applied on a block moving in one dimension is producing a constant power,then the motion should be uniformly accelerated. Reason This constant power multiplied with time is equal to the change in kinetic energy.