Download - 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!