It is desirable that the standards of units be easily available, invariable, indestructible and easily reproducible. If we use foot of a person as a standard unit of length, which of theabove features are present and which are not?

Internal micrometer is a measuring intrument used to measure internal diameter (ID) of a large cylinder bore with high accuracy. Construction is shown in figure. There is one fixed rod B (to the right in figure) and one moved rod A (to the left in figure). It is based on the particle of advancement of a screw when it is rotated in a nut with internal threads. Main scale reading can be directly seen on the hub which is fixed with respect to rod B. When the cap is rotated rod A moves in or cut depending on direction of rotation. The circular scale reading is seen by checking which division of circular scale coincide with the references line This is to be multiplied by LC to get circular scale reading. Least count = value of 1 circular scale division = ("pitch")/("number of division on circular scale") Length of rod A is chosen to match the ID(PQ) to be measured. Zero error is checked by taking reading between standard blocks fixed at normal value of ID to be measured. Zero error is positive if cap end is one the right of the main scale and negative it is on the left side. In the above instrument, while measuring an internal diameter. ID is set of 321 mm with no zero error. It cap end is after n^(th) division adn 17^(th) division of main scale coincides with the reference line, the ID is -

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 )

Internal micrometer is a measuring intrument used to measure internal diameter (ID) of a large cylinder bore with high accuracy. Construction is shown in figure. There is one fixed rod B (to the right in figure) and one moved rod A (to the left in figure). It is based on the particle of advancement of a screw when it is rotated in a nut with internal threads. Main scale reading can be directly seen on the hub which is fixed with respect to rod B. When the cap is rotated rod A moves in or cut depending on direction of rotation. The circular scale reading is seen by checking which division of circular scale coincide with the references line This is to be multiplied by LC to get circular scale reading. Least count = value of 1 circular scale division = ("pitch")/("number of division on circular scale") Length of rod A is chosen to match the ID(PQ) to be measured. Zero error is checked by taking reading between standard blocks fixed at normal value of ID to be measured. Zero error is positive if cap end is one the right of the main scale and negative it is on the left side. In an internal micrometer, main scale division is of 0.5 mm and there are 50 divisions in circular scale. The least count of the instrument is-

Internal micrometer is a measuring intrument used to measure internal diameter (ID) of a large cylinder bore with high accuracy. Construction is shown in figure. There is one fixed rod B (to the right in figure) and one moved rod A (to the left in figure). It is based on the particle of advancement of a screw when it is rotated in a nut with internal threads. Main scale reading can be directly seen on the hub which is fixed with respect to rod B. When the cap is rotated rod A moves in or cut depending on direction of rotation. The circular scale reading is seen by checking which division of circular scale coincide with the references line This is to be multiplied by LC to get circular scale reading. Least count = value of 1 circular scale division = ("pitch")/("number of division on circular scale") Length of rod A is chosen to match the ID(PQ) to be measured. Zero error is checked by taking reading between standard blocks fixed at normal value of ID to be measured. Zero error is positive if cap end is one the right of the main scale and negative it is on the left side. During zero setting of the above instrument, the end of the cap is on left side of the zero of main scale (i.e. zero of main scale is not visible) and 41^(th) division of circular scale coincides with the reference line, the zero error is -

A calorie is a unit of heat or energy and it equals about 4.2 J, where 1 J = 1 kg m^(2) s^(-2) . Suppose we employ a system of units in which the unit of mass equals alpha kg , the unit of length equals is beta m , the unit of time is gamma s . Show tthat a calorie has a magnitude 4.2 alpha^(-1) beta^(-1) gamma^(2) in terms of the new units.

There is another useful system of units, besides the SI/mKs. A system, called the cgs (centimeter-gram-second) system. In this system Coloumb's law is given by vecF =(Qq)/(r^(2)).hatr where the distance is measured in cm (= 10^(-2) m), F in dynes (= 10^(-5) N) and the charges in electrostatic units (es units), where 1 es unit of charge 1/(3) xx 10^(-9) C . The number [3] actually arises from the speed of light in vacuum which is now taken to be exactly given by c = 2.99792458 xx 10^8 m/s. An approximate value of c then is c = [3] xx 10^8 m/s. (i) Show that the coloumb law in cgs units yields 1 esu of charge = 1 (dyne) 1/2 cm. Obtain the dimensions of units of charge in terms of mass M, length L and time T. Show that it is given in terms of fractional powers of M and L. (ii) Write 1 esu of charge = x C, where x is a dimensionless number. Show that this gives: 1/(4piepsilon_(0)) = 10^(-9)/x^(2) (Nm^(2))/C^(2) with x=1/[3] xx 10^(-9) , we have 1/(4pi epsilon_(0)) = [3]^(2) xx 10^(9) (Nm^(2))/C^(2) or 1/(4pi epsilon_(0)) = (2.99792458)^(2) xx 10^(9) (Nm^(2))/C^(2) (exactly).

A calorie is a unit of heat (energy in transit) and it equals about 4.2 J where 1J= 1 kg m^(2) s^(-2) . Suppose we employ a system of units in which the unit of mass equals alpha kg, the unit of length equals beta m, the unit of time is gamma s. Show that a calorie has a magnitude 4.2 alpha^(-1)beta^(-2)gamma^(2) in terms of the new units.