what is dimension of A in a given equation were
F=Av
we're f is force ,v is velocity and a ks aceration?
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Answer:
Let M = (some Number) (V)
a
(F)
b
(T)
c
Equating dimensions of both the sides
M
1
L
0
T
0
=(1)[L
1
T
−1
]
a
[M
1
L
1
T
−2
]
b
[T
1
]
c
M
1
L
0
T
0
=M
b
L
a+b
T
−a−2b+c
get a = - 1, b = 1, c = 1
M = (Some Number) (V
−1
F
1
T
1
)⇒[M]=[V
−1
F
1
T
1
]
Similarly, we can also express energy in terms of V, F, T
Let [E] = [some Number] [V]
a
[F]
b
[T]
c
⇒[ML
2
T
−2
]=[M
0
L
0
T
0
][LT
−1
]
a
[MLT
−2
]
b
[T]
c
[M
1
L
2
T
−2
]=[M
b
L
a+b
T
−a−2b+c
]
⇒ 1 = b; 2 = a + b ; -2 = -a - 2b + c
get a = 1 ; b = 1 ; c = 1
∴ E = (some Number) V
1
F
1
T
1
or[E]=[V
1
][F
1
][T
1
]
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