Question

if 'h' is height and 'g' is acceleration due to gravity , then the dimensional formula of √2h/g is the same as that of options a time b mass c volume d velocity​

Answer 1

Answer:

Correct option is

A

Velocity

Since λ is wavelength, hence its dimension is that of length = L.

Dimension of g is LT−2

Thus, dimension of λg=L2T−2=LT−1, which represents velocity.

Explanation:

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Answer 2

Given:

$\sqrt{ \dfrac{2h}{g} }$

This expression is given.

To find:

Dimensions of the expression is equivalent to?

Calculation:

• Let L be length and T be time. Hence, 'h' represents L and 'g' represents acceleration as L/T².

• The dimensional analysis will be done as follows:

$\bigg[ \sqrt{ \dfrac{2h}{g} } \: \bigg]$

$= \bigg[ \sqrt{ \dfrac{L}{L{T}^{ - 2} } } \: \bigg]$

$= \bigg[ \sqrt{ \dfrac{1}{{T}^{ - 2} } } \: \bigg]$

$= \bigg[ \sqrt{ {T}^{ 2} } \: \bigg]$

$= \bigg[ T \: \bigg]$

So, the dimension is equivalent to TIME (option a)