Qn2. Supposing that: [period] = [mx] [lg] [gz]. Find the value of: a) (i) X (ii) y (iii) z

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ScanSolve AI Tutor · Accepted Answer

here's the solution to your question:

a) To find the values of $x$ , $y$ , and $z$ , we use dimensional analysis.
The dimensions of the quantities are:

The given relationship is $[period] = [m^x][l^y][g^z]$ .
Substituting the dimensions:

[T] = [M^x][L^y][(LT^{-2})^z]

[M^0 L^0 T^1] = [M^x L^y L^z T^{-2z}]

[M^0 L^0 T^1] = [M^x L^{y+z} T^{-2z}]

Now, we equate the exponents of M, L, and T on both sides:
For M: $x = 0$
For L: $y+z = 0$
For T: $1 = -2z$

Solve for $x$ .
From the exponent of M:
$x = 0$
The value of $x$ is $\boxed{\text{0}}$ .
Solve for $z$ .
From the exponent of T:
$1 = -2z$ $z = -\frac{1}{2}$
The value of $z$ is $\boxed{-\frac{1}{2}}$ .
Solve for $y$ .
From the exponent of L:
$y+z = 0$
Substitute the value of $z$ :
$y + \left(-\frac{1}{2}\right) = 0$ $y = \frac{1}{2}$
The value of $y$ is $\boxed{\frac{1}{2}}$ .

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