What are the dimensions of the quantity
lig, 1 being the length and g the
acceleration due to gravity?
Answers
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]
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Answer:
solution : we know,
dimension of length , l = [L]
dimension of acceleration due to gravity, g = [LT-²]
given expression is l\sqrt{\frac{l}{g}
so, dimension of l\sqrt{\frac{l}{g}}l
g
l
=\textbf{dimension of l}\times\sqrt{\frac{\textbf{ dimension of l}}{\textbf{dimension of g}}}=dimension of l×
dimension of g
dimension of l
= [L]\sqrt{\frac{[L]}{[LT^{-2}]}}=[L]
[LT
−2
]
[L]
= [L]\sqrt{[T^2]}=[L]
[T
2
]
= [LT]
so, dimension of l\sqrt{\frac{l}{g}}l
g
l
is [LT]
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