Please I need help on this problem. This is an assignment for Engineering Fundam

Question

Please I need help on this problem. This is an assignment for Engineering Fundamental class, but this assignment is related with physic calculus "Dimensional Analysis". I have not yet taken any physic calculus classes. I have several problems like this but I want to see how to solve them if you could please explain to me step by step that would be greatly appreciated. Here is the problem. The following equations is written in terms of their base dimensions, with the exception of an unknown parameter, k. Determine the required dimensions of k to make the equation dimensionally consistent.
m(L^1)t^2 = k(L^2)t^2 Please I need help on this problem. This is an assignment for Engineering Fundamental class, but this assignment is related with physic calculus "Dimensional Analysis". I have not yet taken any physic calculus classes. I have several problems like this but I want to see how to solve them if you could please explain to me step by step that would be greatly appreciated. Here is the problem. The following equations is written in terms of their base dimensions, with the exception of an unknown parameter, k. Determine the required dimensions of k to make the equation dimensionally consistent.
m(L^1)t^2 = k(L^2)t^2 Here is the problem. The following equations is written in terms of their base dimensions, with the exception of an unknown parameter, k. Determine the required dimensions of k to make the equation dimensionally consistent.
m(L^1)t^2 = k(L^2)t^2

Explanation / Answer

Here,

for the equation to be dimensionally consistent

both sides should have same dimensions

hence , dimensions of m(L^1)t^2 = dimenesions of k(L^2)t^2

m * L * t^2 = k * L^2 * t^2

k = L^-1 * m

the dimension of k must be m * L^-1

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