For the following dimensional equations, find the base dimensions of the paramet

Question

For the following dimensional equations, find the base dimensions of the parameter k: nn
a) MLt^-2 = kM(L^-1)(t^-2)

b) ML(t^-2)(L^-1) = kLt^-3

c) (L^2)(t^-2) = k(M^4)(T^2)

d) M(L^2)(t^-3) = k LT

e) nL(L^3)k = (T^2)(M^-2)L

f) M(I^2)k = nT(M^-3)(L^-1)

g) I(L^2)t = (k^2)(M^4)(t^2)

h) (k^3)(T^6)(M^3)(L^-5) = (T^-3)(t^-6)L

I) (T^(-1/2))(L^-1)(I^2) = (k^(-1/2))(t^4)(T^(-5/2))(L^-3)

J) ML(t^-2) = ML(t^-2) sin(k(L^-2)(M^-1))

K) (T^2)n = (T^2)n ln(kn(T^-1))


Please show some work!! this one really got me so thanks for any help!! =]

Explanation / Answer

a) MLt^-2 = kM(L^-1)(t^-2) k= L^2 b) ML(t^-2)(L^-1) = kLt^-3 k=Mt c) (L^2)(t^-2) = k(M^4)(T^2) k=M^-4L^2 t^-4 d) M(L^2)(t^-3) = k LT k=MLT^-3 f) M(I^2)k = nT(M^-3)(L^-1) k=n M^-4 L^-1 I^-2 T h) (k^3)= (T^-3)(t^-6)L (T^-6)(M^-3)(L^5 ) I) (T^(-1/2))(L^-1)(I^2)(t^-4)(T^(5/2))(L^3) = (k^(-1/2)) K) (T^2)n exp^(T^2)n =(kn(T^-1))

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