chapter 1 - basic physics tutorial

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    BASIC PHYSICS

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    Example 1

    - Write down the dimensions of

    a) Acceleration? [LT-2

    ]b) Energy? [ML2T-2]

    c) ower? [ML2T-!]

    d) Moment"m? [MLT-#]

    e) Electric $harge? [AT]

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    Example 2

    - The %o"ng&s mod"l"s E of a solid is gi'en by

    where

    E  is the %o"ng(s mod"l"s mod"l"s of elasticity)

    F  is the force e*erted on an ob+ect "nder tension, A0  is the original cross-sectional area thro"gh which the force is alied,

     ΔL is the amo"nt by which the length of the ob+ect changes,

    L0  is the original length of the ob+ect.

    /ind the dimensions of %o"ng&s mod"l"s.

     Answer0[ML-#T-2]

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    Example 3

    - /or an ob+ect mo'ing with "niform acceleration1 the 'elocity ' is

    gi'en by the e"ation '2 3 4 *1 where is constant and * is a

    'ariable.

    What are the dimensions of term *?

     Answer0

    [L2T-2]

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    Example 4

    - The e"ation for real gases may be e*ressed as follows0

    4 a562

    )6 7 b) 3 n8T where 3 ress"re1 6 3 'ol"me1 T 3 absol"tetemerat"re1 n3 n"mber of moles and 8 3 molar gas constant.

    What are the dimensions of a and b?

     Answer0

    9imension of a is [ML:T-2] and b is [L!]

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    Example 5

    - The dimensions of the base "antities of length1 mass1 time1 amo"nt

    of s"bstance and temerat"re are denoted by the symbols L1 M1 T1

    ; and < resecti'ely. What are the dimensions of 8 in the e"ation

    6 3 n8T?

    [9imensions of 0 ML-#T-21 60 L!1 n0;1 T0

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    Example 6

    - /ermi energy Ef  is a concet in "ant"m mechanics. =t is the energy

    of the highest occ"ied "ant"m state in a system of fermions at

    >ero temerat"re. /ermi energy of a metal can be related to other

    'ariables by Ef 3 hambnc 1 where is a constant of roortionality1 h 

    is a lanc constant1 m is the mass of an electron1 n is the n"mber

    of free electrons er "nit 'ol"me. 9etermine by dimensional analysis

    the 'al"es of a1 b and c .

    [@nit for lanc constant h0 s]

     Answer0

    a = 2 1 b 3 -# and c = 2/3

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    Example 7

    - $hange the following "nit.

    a) B2CC m h-2

     3 DDDDD. m s-2

    b) #2: cm! 3 DDDDD. m!

    c) 2C g m s-2 3 DDDDD.g cm min-2

    d) C. g cm-! 3 DDDDD.g m-!

    e) 2C cm min-# 3 DDDDD.m s-#

     Answer0

    a) C.::F

    b) #.2: * #C-G

    c) B.2 * #CH

    d) CCC

    e) !.!! * #C-G

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    Example 8

    - The diameter of a shere is meas"red as F.2 cm. What is its

    'ol"me in cm!1 m!1 mm!?

     Answer 

    #C!B cm!1 #.C!B * #C-! m!1 #.C!B * #CF mm!