Question

Let z²=Fr/m, where m is mass and F is force and r is distance. The dimension of z is

Answer 1

Solution :

Given Equation,

$\sf{ {z}^{2} = \dfrac{Fr}{m} }$

To finD

Dimensional Formula of Z

The given equation can also be expressed as,

$\displaystyle{\implies \sf z = \sqrt{ \dfrac{Fr}{m} } }$

$\sf F \longrightarrow ML T^{-2} \\ \\ \sf r \longrightarrow L \\ \\ \sf m \longrightarrow M$

Now,

$\sf{z = ( \dfrac{ \cancel{M}L {T}^{ - 2} \times l }{ \cancel{M}}) {}^{ \frac{1}{2} } } \\ \\ \implies \: \sf{z = ({L}^{2} {T}^{ - 2} ) {}^{ \frac{1}{2} } } \\ \\ \implies \: \boxed{ \boxed{\sf{z = LT}}}$

The dimensional formula of Z is [L¹T¹]