{"id":8023,"date":"2025-04-13T11:31:04","date_gmt":"2025-04-13T11:31:04","guid":{"rendered":"https:\/\/physicsera.com\/?p=8023"},"modified":"2025-07-01T05:48:06","modified_gmt":"2025-07-01T05:48:06","slug":"measurment","status":"publish","type":"page","link":"https:\/\/physicsera.com\/?page_id=8023","title":{"rendered":"MEASURMENT-MCQS"},"content":{"rendered":"

\"\"<\/h4>\n

QUICK REVIEW<\/strong><\/span><\/h3>\n

PHYSICS<\/strong><\/span><\/h4>\n

Physics is the branch of science that studies the nature and behavior of matter, energy, and the interaction between them<\/span><\/h4>\n

\u00a0The main Branches of Physics<\/span><\/span><\/strong><\/span>
\nPhysics is constituted of many interdisciplinary subjects and branches for those interested in<\/span>
\nmaking a career in this field. Here are all branches of Physics:<\/span>
\n1. Classical Physics<\/span>
\n2. Modern Physics<\/span>
\n3. Nuclear Physics<\/span>
\n4. Atomic Physics<\/span>
\n5. Geophysics<\/span>
\n6. Biophysics<\/span>
\n7. Mechanics<\/span>
\n8. Acoustics<\/span>
\n9. Optics<\/span>
\n10. Thermodynamics<\/span>
\n11. Astrophysics<\/span><\/p>\n

INTERNATIONAL SYSTEM OF UNITS (SI)<\/strong><\/span><\/p>\n

.<\/span><\/p>\n\n\n\n\n\n\n\n\n\n\n
Basic quantity<\/strong><\/span><\/td>\nSymbol of Basic Quantity<\/strong><\/span><\/td>\nName of the Base SI units<\/strong><\/span><\/td>\nSymbol of\u00a0<\/strong>SI units<\/strong><\/span><\/td>\n<\/tr>\n
Time<\/strong><\/span><\/td>\nT<\/strong><\/span><\/td>\nSecond<\/strong><\/span><\/td>\ns<\/strong><\/span><\/td>\n<\/tr>\n
Length<\/strong><\/span><\/td>\nL<\/strong><\/span><\/td>\nMetre<\/strong><\/span><\/td>\nm<\/strong><\/span><\/td>\n<\/tr>\n
Mass<\/strong><\/span><\/td>\nM<\/strong><\/span><\/td>\nKilogram<\/strong><\/span><\/td>\nkg<\/strong><\/span><\/td>\n<\/tr>\n
Temperature<\/strong><\/span><\/td>\nT, \u03b8<\/strong><\/span><\/td>\nKelvin<\/strong><\/span><\/td>\nK<\/strong><\/span><\/td>\n<\/tr>\n
Electric current<\/strong><\/span><\/td>\nI<\/strong><\/span><\/td>\nAmpere<\/strong><\/span><\/td>\nA<\/strong><\/span><\/td>\n<\/tr>\n
Amount of substance<\/strong><\/span><\/td>\nn<\/strong><\/span><\/td>\nMole<\/strong><\/span><\/td>\nmol<\/strong><\/span><\/td>\n<\/tr>\n
Luminous intensity<\/strong><\/span><\/td>\nlv<\/sub><\/strong><\/span><\/td>\nCandela<\/strong><\/span><\/td>\ncd<\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

PREFIXES FOR SI UNITS<\/strong><\/span><\/h4>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Value<\/strong><\/span><\/td>\nPrefix<\/strong><\/span><\/td>\nSymbol<\/strong><\/span><\/td>\n<\/tr>\n
1024<\/sup><\/strong><\/span><\/td>\nyotta<\/strong><\/span><\/td>\nY<\/strong><\/span><\/td>\n<\/tr>\n
1021<\/sup><\/strong><\/span><\/td>\nZetta<\/strong><\/span><\/td>\nZ<\/strong><\/span><\/td>\n<\/tr>\n
1018<\/sup><\/strong><\/span><\/td>\nexa-<\/strong><\/span><\/td>\nE<\/strong><\/span><\/td>\n<\/tr>\n
1015<\/sup><\/strong><\/span><\/td>\npeta-<\/strong><\/span><\/td>\nP<\/strong><\/span><\/td>\n<\/tr>\n
1012<\/sup><\/strong><\/span><\/td>\ntera-<\/strong><\/span><\/td>\nT<\/strong><\/span><\/td>\n<\/tr>\n
109<\/sup><\/strong><\/span><\/td>\ngiga-<\/strong><\/span><\/td>\nG<\/strong><\/span><\/td>\n<\/tr>\n
106<\/sup><\/strong><\/span><\/td>\nmega-<\/strong><\/span><\/td>\nM<\/strong><\/span><\/td>\n<\/tr>\n
103<\/sup><\/strong><\/span><\/td>\nkilo-<\/strong><\/span><\/td>\nK<\/strong><\/span><\/td>\n<\/tr>\n
102<\/sup><\/strong><\/span><\/td>\nhecto-<\/strong><\/span><\/td>\nh<\/strong><\/span><\/td>\n<\/tr>\n
101<\/sup><\/strong><\/span><\/td>\ndeca-<\/strong><\/span><\/td>\nda<\/strong><\/span><\/td>\n<\/tr>\n
10-1<\/sup><\/strong><\/span><\/td>\ndeci-<\/strong><\/span><\/td>\nd<\/strong><\/span><\/td>\n<\/tr>\n
10-2<\/sup><\/strong><\/span><\/td>\ncenti-<\/strong><\/span><\/td>\nc<\/strong><\/span><\/td>\n<\/tr>\n
10-3<\/sup><\/strong><\/span><\/td>\nmilli-<\/strong><\/span><\/td>\nm<\/strong><\/span><\/td>\n<\/tr>\n
10-6<\/sup><\/strong><\/span><\/td>\nMicro<\/strong><\/span><\/td>\n\u03bc <\/strong><\/span><\/td>\n<\/tr>\n
10-9<\/sup><\/strong><\/span><\/td>\nnano-<\/strong><\/span><\/td>\nn<\/strong><\/span><\/td>\n<\/tr>\n
10-12<\/sup><\/strong><\/span><\/td>\npico-<\/strong><\/span><\/td>\np <\/strong><\/span><\/td>\n<\/tr>\n
10-15<\/sup><\/strong><\/span><\/td>\nfemto-<\/strong><\/span><\/td>\nf<\/strong><\/span><\/td>\n<\/tr>\n
10-18<\/sup><\/strong><\/span><\/td>\natto-<\/strong><\/span><\/td>\na<\/strong><\/span><\/td>\n<\/tr>\n
10-21<\/sup><\/strong><\/span><\/td>\nzepto<\/strong><\/span><\/td>\nz<\/strong><\/span><\/td>\n<\/tr>\n
10-24<\/sup><\/strong><\/span><\/td>\nyocto<\/strong><\/span><\/td>\ny<\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

SUPPLEMENTARY UNIT:<\/strong><\/span><\/p>\n

\"\"<\/span><\/p>\n

DIMENSION<\/strong><\/span><\/h2>\n

The dimension of a physical quantity is the power of the fundamental quantities in terms of which it can be represented. Each of the basic quantities is called \u201c dimension\u201d\u00a0 Or<\/span><\/p>\n

The word dimension has a special meaning in physics. It is used to denote the nature of the physical quantity<\/span>.<\/em><\/strong>\u00a0<\/em><\/strong><\/span><\/p>\n\n\n\n\n\n\n\n\n
DIMENSION<\/strong><\/span><\/td>\nSymbol <\/strong><\/span><\/td>\n<\/tr>\n
Time<\/strong><\/span><\/td>\n[T]<\/strong><\/span><\/td>\n<\/tr>\n
Length<\/strong><\/span><\/td>\n[L]<\/strong><\/span><\/td>\n<\/tr>\n
Mass<\/strong><\/span><\/td>\n[M]<\/strong><\/span><\/td>\n<\/tr>\n
Temperature<\/strong><\/span><\/td>\n[T], [\u03b8]<\/strong><\/span><\/td>\n<\/tr>\n
Electric current<\/strong><\/span><\/td>\n[A]<\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"\"<\/p>\n

SIGNIFICANT FIGURES<\/strong><\/span><\/h2>\n
The number of accurately known digit and first doubtful digit( called least significant)<\/span><\/h5>\n
are known as significant figures or significant digit.<\/span><\/h5>\n

RULES OF DETERMINATION SIGNIFICANT FIGURES <\/u><\/strong><\/span><\/p>\n

ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are ALWAYS significant<\/strong><\/span><\/p>\n

EXAMPLE<\/strong><\/span><\/p>\n

    \n
  • 3423\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (ii)\u00a0\u00a0\u00a0\u00a0 457435\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/li>\n<\/ul>\n

    4- significant figure\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 6 -significant figure\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

    (iii)\u00a0\u00a0\u00a0 587\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (iv) 58<\/span><\/p>\n

    3- significant figure\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2- significant figure<\/span><\/p>\n

    ALL zeroes between non-zero numbers are ALWAYS significant<\/strong><\/span><\/p>\n

    EXAMPLE<\/strong><\/span><\/p>\n

      \n
    • 3003\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (ii)\u00a0\u00a0\u00a0\u00a0 009\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/li>\n<\/ul>\n

      4- significant figure\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 5 -significant figure<\/span><\/p>\n

      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (iii)\u00a0\u00a0\u00a0 507\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (iv)\u00a0\u00a0 5000097\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

      3- significant figure\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3- significant figure<\/span><\/p>\n

       <\/p>\n

      Zeros locating the position of decimal in numbers of magnitude less than one are not significant<\/span><\/p>\n

      EXAMPLE<\/strong><\/span><\/p>\n

        \n
      • 0063\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (ii)\u00a0\u00a0\u00a0\u00a0 0.009\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/li>\n<\/ul>\n

        2- significant figure\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1 -significant figure<\/span><\/p>\n

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (iii)\u00a0\u00a0\u00a0 0.0000307\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (iv) 0.0009078<\/span><\/p>\n

        3- significant figure\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4 -significant figure<\/span><\/p>\n

        Final zeros to the right of the decimal point are significant.<\/span><\/p>\n

        EXAMPLE<\/strong><\/span><\/p>\n

          \n
        • 0500\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (ii)\u00a0\u00a0\u00a0\u00a0 0.00900\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/li>\n<\/ul>\n

          5- significant figure\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3 -significant figure<\/span><\/p>\n

          (iii)\u00a0\u00a0\u00a0 9.00300\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (iv) 0.090200<\/span><\/p>\n

          6- significant figure\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 5- significant figure<\/span><\/p>\n

           <\/p>\n

          Zeros at the end of the numbers greater than one may are may not be significant<\/span><\/p>\n

          EXAMPLE<\/strong><\/span><\/p>\n

            \n
          • 700\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (ii)\u00a0\u00a0\u00a0\u00a0 980000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/li>\n<\/ul>\n

            1- significant figure\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2- significant figure<\/span><\/p>\n

            \u00a0For any value written in scientific notation as A<\/em> \u00d7 10x<\/sup><\/strong><\/em>, the number of significant figures is determined by applying the above rules only to the value of\u00a0A.<\/em><\/span><\/p>\n

            EXAMPLE<\/strong><\/span><\/p>\n

            4.5 \u00d7 103\u00a0<\/sup>has two significant figures<\/span><\/p>\n

            4.50 \u00d7 10-9<\/sup>\u00a0has three significant figures<\/span><\/p>\n

            4.500 \u00d7 1023<\/sup>\u00a0has four significant figures<\/span><\/p>\n

            COMBINING UNCERTAINTY: ADDING AND SUBTRACTING <\/strong><\/span><\/p>\n

            Q-1\u00a0 \u00a0 The length of a copper wire at 30\u00b0C is 18.2 \u00b1 0.04 cm and at 60\u00b0C is 19.7 \u00b1 0.02 cm. Find the absolute uncertainty and die extension of the wire.<\/span><\/strong><\/span><\/p>\n

            DATA<\/strong><\/span><\/p>\n

            The length\u00a0 L1 <\/sub>\u00a0= 18.2 \u00b1 0.04<\/span><\/p>\n

            The length\u00a0 L2 <\/sub>\u00a0= 19.7 \u00b1 0.02<\/span><\/p>\n

            \u00a0<\/strong><\/span>SOLUTIONS<\/strong><\/span><\/span><\/p>\n

            \u00a0<\/strong><\/span>Extension of the wire<\/strong><\/span><\/span><\/p>\n

            L = \u00a0(L2\u00a0\u00a0\u00a0 <\/sub>–\u00a0 L1 <\/sub>) <\/strong><\/span><\/p>\n

            L = (19.7-18.2)\u00a0 <\/strong><\/span><\/p>\n

            L\u00a0 = \u00a01.5mm <\/strong><\/span><\/p>\n

            Absolute uncertainty<\/strong><\/span><\/p>\n

            \u2206L =\u00a0 \u2206L1<\/sub>\u00a0 +\u00a0 \u2206L2<\/sub><\/strong><\/span><\/p>\n

            \u00a0<\/strong><\/span>\u2206L = 0.04 +0.02 <\/strong><\/span><\/span><\/p>\n

            \u2206L = 0.06<\/strong><\/span><\/p>\n

            Extension of the wire with uncertainty = (\u00a0 L\u00a0 \u00b1\u00a0 \u2206L ) <\/strong><\/span><\/p>\n

            Extension of the wire with uncertainty = ( 1.5\u00a0\u00a0 \u00b1\u00a0 0.06 ) mm<\/strong><\/span><\/p>\n

            Q-<\/strong>\u00a0 \u00a0w = (4.52 \u00b1 0.02) cm, x = ( 2.0 \u00b1 0.2) cm, y = (3.0 \u00b1 0.6) cm. Find z = x + y – w and<\/strong><\/span><\/p>\n

            its uncertainty.<\/strong><\/span><\/p>\n\n\n\n
            DATA<\/strong><\/span><\/p>\n

            w = (4.52 \u00b1 0.02) cm<\/strong><\/span><\/p>\n

            x = ( 2.0 \u00b1 0.2) cm<\/strong><\/span><\/p>\n

            y = (3.0 \u00b1 0.6) cm<\/strong><\/span><\/p>\n

            SOLUTIONS<\/strong><\/span><\/p>\n

            Dz =\u00a0Dx +\u00a0Dy +\u00a0Dw <\/strong><\/span><\/p>\n

            Dz\u00a0 = 0.2 + 0.6 + 0.02 <\/strong><\/span><\/p>\n

            Dz = 0.82\u00a0 <\/strong><\/span><\/td>\n

            		So\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 z = x +y -w<\/strong><\/span><\/p>\n

            \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 z = 2.0 \u00a0+3.0 \u00a0-4.52 \u00a0\u00a0\u00a0<\/strong><\/span><\/p>\n

            \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 z = 5.0\u00a0 -4.52\u00a0\u00a0\u00a0\u00a0 <\/strong><\/span><\/p>\n

            \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 z = 0.48 cm<\/strong><\/span><\/p>\n

            Answer with uncertainty<\/strong><\/span><\/p>\n

            \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Z\u00a0 =\u00a0 (z\u00a0 \u00a0\u00b1 \u2206z ) cm<\/strong><\/span><\/p>\n

            \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Z\u00a0 =\u00a0 (0.48 \u00b1 0.82) cm<\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

            Q-\u00a0 \u00a0 Three objects have masses of 3 \u00b1 0.1 kg, 7 \u00b1 0.1 kg, and 4 \u00b1 0.05 kg. What is the uncertainty in the total mass of the three objects?\u00a0<\/strong><\/span><\/p>\n\n\n\n
            DATA<\/strong><\/span><\/p>\n

            m1<\/sub> = (3 \u00b1 0.1\u00a0) kg <\/strong><\/span><\/p>\n

            m2<\/sub> = (7 \u00b1 0.1\u00a0) kg<\/strong><\/span><\/p>\n

            m3\u00a0 =\u00a0 (<\/sub>4 \u00b1 0.05) kg<\/strong>\u00a0<\/span><\/p>\n

            SOLUTIONS<\/strong>.<\/span><\/p>\n

            m \u00a0= <\/strong>m1<\/sub><\/strong> + <\/strong>m1 + <\/sub>m1<\/sub><\/strong> =<\/strong><\/span><\/p>\n

            m =\u00a0 \u00a03 + \u00a07\u00a0 +\u00a0 4 \u00a0= 14 kg<\/strong><\/span><\/td>\n

            		\u2206m = \u2206 <\/strong>m1<\/sub>\u00a0 +\u00a0 <\/strong>\u00a0\u2206 <\/strong>m2<\/sub> + <\/strong>\u00a0\u2206 <\/strong>m3<\/sub><\/strong><\/span><\/p>\n

            \u2206m =\u00a0 0.1 + 0.1 + 0.05 <\/strong><\/span><\/p>\n

            \u2206m =\u00a0 0.25 <\/strong><\/span><\/p>\n

            Answer with uncertainty<\/strong><\/span><\/p>\n

            \u00a0 =\u00a0\u00a0 m\u00a0 <\/strong>\u00b1\u00a0 <\/strong>\u2206m<\/strong><\/span><\/p>\n

            \u00a0 =\u00a0\u00a0 (14\u00a0 <\/strong>\u00b1\u00a0 <\/strong><\/span>0.25 )<\/span> k<\/span>g<\/strong><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

             <\/p>\n