Given m = N$\sqrt{\frac{SL}{T}}$ make T the subject of the formula

To make $T$ the subject of the formula $m = N\sqrt{\frac{SL}{T}}$, follow these steps:

1. Analyze the equation

We have $m = N\sqrt{\frac{SL}{T}}$. Our goal is to isolate $T$ on one side of the equation.

2. Explain the concept

To isolate a variable inside a square root, we must first eliminate the root by squaring both sides. Then, we use algebraic manipulation (cross-multiplication and division) to move the variables until $T$ stands alone.

3. Step-by-step solution

Step 1: Divide both sides by $N$

Step 2: Square both sides to remove the square root

Step 3: Cross-multiply to bring $T$ to the numerator

Step 4: Divide both sides by $m^2$ to isolate $T$

(Note: In your question, the variable $m$ is written as lowercase in the equation but uppercase in the options. Based on standard algebraic conventions, we treat them as the same variable.)

4. Identify the answer

Comparing our result $T = \frac{N^2SL}{m^2}$ with the given options, it matches option B.

5. Exam Tip

When dealing with formulas involving square roots, always remember to square the entire side of the equation, not just the individual terms inside. A common mistake is writing $\frac{m^2}{N}$ instead of $\frac{m^2}{N^2}$. Always distribute the exponent to every factor in the fraction!