Question

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

Answer 1

Answer:

dimensions of l=√dimension of l/dimensions of g =√m/m/s^. =√l/l.t-1 = √t^

Answer 2

Answer:

The dimensions of the quantity is $LT^{-1}$

Explanation:

Quantity = $l\sqrt{\frac{l}{g}}$

Using the dimension analysis:

The units for l = m

The units for gravity is $m/s^2$ which when converted to base units give $1/T^2$

$l\sqrt{\frac{l}{l\times{T}^{2}}} = l\sqrt{\frac{1}{T^2}}\\\\=L/T$

$=LT^{-1}$

Dimensional analysis involves expressing units in their simplest form or the fundamental units. A typical example is gravity. The units $m/s^2$ is secondary dimension since it combines units of other quantities while $1/T^2$ expresses gravity in fundamental units. One of the important reasons to use dimensional analysis is to keep to avoid confusing units.