Question

A body falls from rest under gravity, the velocity “v” is given by v=kgp h q , where h is the distance fallen through, g the acceleration of gravity, and k, p and q are constants. Which relation is the one that satisfies the dimensional analysis:

Answer 1

The relation that satisfies the the dimensional analysis is $1[LT^{-1} ]= k[L^{p+q} T^{-2p}]$

Your velocity equation seems to be incorrectly typed, below is the equation is I presume you intended to type;

$v = kg^{p}h^{q}$

The dimensional analysis of the velocity equation is calculated as follows;

$v = kg^{p}h^{q}$

where;

k, p and q are constant

h is the distance (m)

g is acceleration due to gravity (m/s²)

v is the velocity (m/s)

$v = kg^ph^q\\\\LT^{-1} = k[LT^{-2}]^p[L]^q\\\\LT^{-1} = k[L^pT^{-2p}][L^q]\\\\1[LT^{-1} ]= k[L^{p+q} T^{-2p}]\\\\1 = k\\\\L^1 = L^{p+q} \\\\1 = p+q\\\\T^{-1} = T^{-2p}$

Thus, the relation that satisfies the the dimensional analysis is $1[LT^{-1} ]= k[L^{p+q} T^{-2p}]$

Learn more here: brainly.com/question/17224555