Question

What are the dimensions of the quantity l√l/g, l being the length and g is acceleration due to gravity

Answer 1

Answer:

The dimensions of l × √(l/g) are [L][T]

Explanation:

We have to find the dimensions of the quantity

$l\times  \sqrt{l/g}$

We know that

Dimension of length l = $[L]$

Dimensions of acceleration due to gravity g = $[LT^{-2}]$

Therefore, dimensions of l × √(l/g)

$=[L]\times\sqrt{[L]/[LT^{-2}]}$

$=[L]\times\sqrt{[T^{2}]}$

$=[L]\times{[T^{2}]^{1/2}$

$=[L][T]$

Therefore the dimensions of l × √(l/g) are [L][T]

Hope this helps.

Answer 2

your question -> what is the dimension of the quantity l√{l/g} , l being the length and g is the acceleration due to gravity.

solution : 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 $l\sqrt{\frac{l}{g}}$

$=\textbf{dimension of l}\times\sqrt{\frac{\textbf{ dimension of l}}{\textbf{dimension of g}}}$

$= [L]\sqrt{\frac{[L]}{[LT^{-2}]}}$

= $[L]\sqrt{[T^2]}$

= [LT]

so, dimension of $l\sqrt{\frac{l}{g}}$ is [LT]