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Example 2.16 The SI unit of energy is
J = kg m?s that of speed vis ms and
of acceleration a is
m s-2. Which of the
formulae for kinetic energy (K) given below
can you rule out on the basis of
dimensional arguments (m stands for the
mass of the body) :
(a) K = m v
(b) K=(1/2)mm2
(c) K= ma
(d) K = (3/16)mu?
(e) K = (1/2)mu?+ ma
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Answer:
The dimensional formula for K.E is [M
1
L
2
T
−2
]
According to the principle of homogeneity of dimensional analysis, the dimensions of each term on both the sides of correct formula or equation will be the same.
The dimensions of quantity on R.H.S of different quantities are
(a)[M
2
L
3
T
−3
]
(b)[M
1
L
2
T
−2
]
(c)[M
1
L
1
T
−2
]
(d)[M
1
L
2
T
−2
]
(e)[M
1
L
2
T
−2
]+[M
1
L
1
T
−2
]
Since dimensional formula of the R.H.S of (a),(c) and both the terms of R.H.S of (e) are not the same as that of L.H.S i.e.,[M
1
L
2
T
2
]
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