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Why quantities appearing with higher (po...

Why quantities appearing with higher (power) exponent should be measured with most accurately ?

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Relative error due to exponent or (power) is multiplied. Hence, it contribute to more error hence calculation become less accurate hence by measuring these quantities more accurately error due to them can be eliminated.
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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 )

KUMAR PRAKASHAN-UNITS AND MEASUREMENT-SECTION -C (OBJECTIVE QUESTIONS (VSQS)
  1. Why are errors expressed as positive and negative?

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  2. 1 gcm^(-3).... Kgm^(-3) (Fill the gaps)

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  3. Why quantities appearing with higher (power) exponent should be measu...

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  4. Write accuracy of atomic clock.

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  5. If f=x^(2) then what will be relative error in measurement of f ?

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  6. Write six physical quantities which have dimension of M^(1)L^(2)T^(-2)

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  7. Are dimension of mass and weight equal ?

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  8. Write physical quantity having dimension of Nm^(-1)s^(2).

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  9. Is it possible that physical quantity has dimension but do not have mo...

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  10. Explain supplementary quantities and their unit of SI system.

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  11. Which are inferior planets ?

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  12. What is elongation ?

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  13. In modern times which method is used to measure the distance between t...

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  14. "Fundamental unit of length is kilometer and fundamental unit of mass ...

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  15. x=a+bt+ct^(2)=x in metre and tis in sec then write unit of a, b, c.

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  16. Light year is unit of …... .

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

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  18. y=x^(2)r+M^(1)L^(1)T^(-2) is dimensionally correct. If r represent dis...

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  19. Pressure P = FK where F is force, obtain dimension of K.

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  20. Obtain dimension of rho gv where, rho = density, g = acceleration, v...

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