Question

​What are the dimesions of the quantity
\sqrt[1]{1g} 1
1

1g
​
1
$\sqrt[1]{1g}$

being the length and g the acceleration due to gravity?
​

Answer 1

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]