What are the dimensions of the quantity l√l/g , l being the length and g the acceleration due to gravity?
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5
Answer:
The dimensions of l × √(l/g) are [L][T]
Explanation:
We have to find the dimensions of the quantity
l\times \sqrt{l/g}l×
l/g
We know that
Dimension of length l = [L][L]
Dimensions of acceleration due to gravity g = [LT^{-2}][LT
−2
]
Therefore, dimensions of l × √(l/g)
=[L]\times\sqrt{[L]/[LT^{-2}]}=[L]×
[L]/[LT
−2
]
=[L]\times\sqrt{[T^{2}]}=[L]×
[T
2
]
=[L]\times{[T^{2}]^{1/2}
=[L][T]=[L][T]
Therefore the dimensions of l × √(l/g) are [L][T]
Hope this helps.
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