A physical quantity x can dimensionally ...

A physical quantity x can dimensionally represented in terms of M, L and T that is `x=M^(a) L^(b) T^(c)`. The quantity time-

May be dimensionally represented in terms of x, M and L if `c ne 0`

May be dimensionally represented in terms of x, M and L if `c=0`

May be dimensionally represented in terms of x, M and L, irrespective of value of c

Can never be dimensionally represented in terms of x, M and L

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Dimension of a physical quantity is M^(a)L^(b)T^(c) , then it is ......

Match the physical quantities given on column I with dimensions expressed in terms of mass (M) length (L) time (T), and charge (Q) given in column II and write the correct answer against the matched quantity in a tabular form in your answer book. {:("Column-I",,"Column-II"),("Angular momentum",,[ML^(2)T^(-2)]),("Latent heat",,[ML^(2)Q^(-2)]),("Torque",,[ML^(2)T^(-1)]),("Capacitance",,[ML^(3)T^(-1)Q^(-2)]),("Inductance",,[M^(-1)L^(-2)T^(2)Q^(2)]),("Resistivity",,[L^(2)T^(-2)]):}

A physical quantity X is represented by X = (M^(x) L^(-y) T^(-z) . The maximum percantage errors in the measurement of M , L , and T , respectively , are a% , b% and c% . The maximum percentage error in the measurement of X will be

A physical quantity has unit ("Watt")/(m^(2)) write its dimension.

A physical quantity X is related to four measurable quantities a, b, c and d as follows X=a^(2)b^(3)c^((5)/(2))d^(-2) . The percentange error in the measurement of a, b, c and d are 1 %, 2%, 3% and 4% respectively. What is the percentage error in quantity X? If the value of X calculated on the basis of the above relation is 2.763. to what value should you round off the result.

If the dimensions of a physical quantity are given by M^(x) L^(y) T^(z) , then physical quantity may be

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

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. From the concept of directed dimension what is the formula for a range (R) of a cannon ball when it is fired with vertical velocity component V_(y) and a horizontal velocity component V_(x) , assuming it is fired on a flat surface. [Range also depends upon acceleration due to gravity , g and k is numerical constant]

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 )

Assertion : All derived quantities may be represented dimensionally in terms of the base quantities. Reason : The dimensions of a base quantity in other base quantities are always zero.

ALLEN -MISCELLANEOUS-Exercise-02

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