dimension of a and b if f= at^-1 + bt^2
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11th
Physics
Units and Measurement
Dimensions and Dimensional Analysis
A force is given by F = at ...
PHYSICS
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Asked on December 20, 2019 by
Alina Dayal
A force is given by F=at+bt
2
, where t is time, the dimensions of a and b are respectively :
MEDIUM
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ANSWER
⇒ Since F=at+bt
2
−−−(1)
∴ Dimension of at and bt
2
must be equal to force only.
Hence [F]=[M
1
L
1
T
−2
]−−−(2)
F from (1) and (2)
⇒ [at]=a[T]=[F]
∴ a[T]=[M
1
L
1
T
−2
]
∴ [a]=[M
1
L
1
T
−3
]
and per bt
2
=b[T
2
]=[M
1
L
1
T
−2
]
∴
[b]=[M
1
L
1
T
−4
]
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