Physical Quantities and Their Units

MKS stands for Meter - Kilogram - Second, while CGS stands for Centimeter - Gram - Second. The primary difference lies in the units of measurement, where MKS uses meters, kilograms, and seconds, and CGS uses centimeters, grams, and seconds.

Accuracy is the measure of how close a measured value is to the true value of a quantity. For example, hitting the target closely with a rifle shows accuracy.

Precision refers to the resolution or limit at which a quantity is measured by an instrument. For example, if all shots fired from a rifle are grouped closely together but far from the target, it demonstrates precision.

<p>$0.046 N/m^2$ converts to $0.46 ext{ dyne/cm}^2$ by using the conversion factor where $1 N/m^2 = 10^5 dyne/cm^2$. Therefore, $0.046 imes 10^5 dyne/cm^2 = 0.46 dyne/cm^2$.</p> Signup and view all the answers

<p>$1 gm/cm^3$ is equivalent to $1000 kg/m^3$ because $1 gm/cm^3 = 1 imes 10^{-3} (10^{-2})^3 kg/m^3 = 1 imes 10^{3} kg/m^3$.</p> Signup and view all the answers

<p>A physical quantity is a measurable quantity that can describe physical phenomena. Examples include length and mass.</p> Signup and view all the answers

<p>The seven fundamental physical quantities are length, mass, time, electric current, thermodynamic temperature, luminous intensity, and quantity of matter.</p> Signup and view all the answers

<p>Derived physical quantities are those that can be expressed in terms of fundamental quantities. An example is velocity, measured in m/s.</p> Signup and view all the answers

<p>A unit should have a definite and unambiguous measure.</p> Signup and view all the answers

<p>It is important for a unit to remain unchanged over time to ensure consistent measurements regardless of when they are taken.</p> Signup and view all the answers

<p>One practical unit for measuring very small lengths is the nanometer (nm), which is equivalent to $10^{-9}$ m.</p> Signup and view all the answers

<p>One supplementary unit is the radian (rad), which measures the angle subtended at the center of a circle by an arc equal to the circle's radius.</p> Signup and view all the answers

<p>One example of a derived quantity is pressure, calculated using the formula $kg/(m imes s^2)$.</p> Signup and view all the answers

<p>A_cd = ( |Δa_1| + |Δa_2| +...+ |Δa_n| ) / n</p> Signup and view all the answers

<p>The relative error is represented as δa = A_cd / a̅.</p> Signup and view all the answers

<p>Percentage Error = δa x 100%.</p> Signup and view all the answers

<p>Significant figures are the digits that are known reliably plus the first uncertain digit.</p> Signup and view all the answers

<p>There are five significant figures in 0.0069000.</p> Signup and view all the answers

<p>The number of significant figures does not change when changing units.</p> Signup and view all the answers

<p>An example of a physical quantity is length, and its unit can be meters.</p> Signup and view all the answers

<p>If the digit to be dropped is less than 5, the preceding digit stays the same; if more than 5, it is raised by one.</p> Signup and view all the answers

<p>0.01 mm</p> Signup and view all the answers

<p>A positive error occurs when the zero of the circular scale lies below the base line.</p> Signup and view all the answers

<p>+0.07 mm</p> Signup and view all the answers

<p>+0.07 mm</p> Signup and view all the answers

<p>A hollow tube, circular scale, base line, anvils, and a semicircular plate.</p> Signup and view all the answers

<p>Zero error occurs when there is no gap between the anvils, and the zero of the circular scale coincides with the base line.</p> Signup and view all the answers

<p>You would use the least count to measure the additional readings indicated by the circular scale.</p> Signup and view all the answers

<p>Least count = pitch distance / total divisions on the circular scale.</p> Signup and view all the answers

<p>Circular scale reading is calculated as the product of the coinciding mark and the least count. Therefore, it is $99 imes 0.01 ext{ mm} = 0.99 ext{ mm}$.</p> Signup and view all the answers

<p>The thickness of a metallic sheet is calculated as $M.S.R + C.S.R + c'$. Thus, it equals $6 + 0.99 + 0 = 6.99 ext{ mm}$.</p> Signup and view all the answers

<p>Systematic error is a consistent error that can be either positive or negative, and examples include defects in instruments, such as a broken end of a meter scale.</p> Signup and view all the answers

<p>Random errors occur despite using calibrated instruments and can be estimated by taking a large number of observations and applying statistical methods.</p> Signup and view all the answers

<p>The formula for the arithmetic mean is $ar{a} = (a_1 + a_2 + ... + a_n) / n$, representing the true value of the measured physical quantities.</p> Signup and view all the answers

<p>Absolute error is the difference between the true value and an individual measured value, calculated as $ riangle a_1 = ar{a} - a_1$.</p> Signup and view all the answers

<p>Positive error is calculated using the formula: $Positive , Error = + matching , division \times least , count$.</p> Signup and view all the answers

<p>Mean absolute error is the average of the absolute errors of all observations, specifically the mean of the positive values of these absolute errors.</p> Signup and view all the answers

<p>The correction for a positive error of +0.02 cm is -0.02 cm.</p> Signup and view all the answers

<p>Personal errors can occur due to carelessness or improper arrangement of instruments, affecting the reliability of measurement readings.</p> Signup and view all the answers

<p>The least count is defined as $Least , count = \frac{The , value , of , smallest , division , on , main , scale}{total , divisions , on , vernier , scale}$.</p> Signup and view all the answers

<p>To find the outer diameter, you need the main scale reading, Vernier scale reading, and any zero error correction (c').</p> Signup and view all the answers

<p>Negative error indicates that the zero of the vernier scale stands to the left of the main scale, leading to an underestimation of measurements.</p> Signup and view all the answers

<p>Yes, Vernier calipers can be used to measure the inner diameter of hollow objects due to their design, which allows measurements from the inside edges.</p> Signup and view all the answers

<p>The basic principle of a micrometer screw gauge is based on its least count, which allows for precise measurements of small lengths.</p> Signup and view all the answers

<p>A micrometer screw gauge consists of a semicircular steel frame with a screw that moves within cylindrical ends and a hollow tube attached to measure thickness.</p> Signup and view all the answers