Question

a force is given as f= alpha^2/beta .e to the power v/beta where f is the force and v is the velocity the dimensional formula of alpha ^4 beta ^-2​

Answer 1

a force is given as $f=\frac{\alpha^2}{\beta.e^{v/beta}}$

where f is the force , v is the velocity

then, we have to find dimensional formula of $\alpha^4\beta^{-2}$

we know, power of e is a dimensionless quantity. so, $\frac{v}{\beta}$ is dimensionless quantity.

it is possible when dimension of v = dimension of $\beta$ = [LT-¹]

[ as we know, dimension of v = [LT-¹] ]

now dimension of force = [MLT-²]

so, dimension of f = dimension of $\frac{\alpha^2}{\beta}$

or, [MLT-²] = dimension of $\alpha^2$/[LT-¹]

or, dimension of $alpha^2$ = [ML²T-³]

so, dimension of $\alpha^4\beta^{-2}$= [ML²T-³]² × [LT-¹]^{-2}

= [M²L⁴T^-6]/[L²T-²]

= [M²L²T-⁴] This is the required answer.

Answer 2

Explanation:

hope this will be help you dear

plz mark me as brainalist

have a great day