Question

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

Answer 1

dimension of l\sqrt{\frac{l}{g}}l

g

l

is [LT]

Explanation:

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]