If $\frac{t}{L}$ = $\sqrt{(\frac{4\pi^2}{g}})$, what is the value of g when L = 4.5; t = 5 secs

Analyze the question: We are given t/L = √(4π²/g) and need g when L = 4.5 and t = 5. The plan is to make g the subject of the formula, then substitute.

Concept: To remove a square root, square both sides. Then rearrange to isolate g.

Step 1: Square both sides

(t/L)² = 4π²/g

Step 2: Make g the subject

g = 4π² · (L/t)² = 4π²L²/t²

Step 3: Substitute the values (π ≈ 3.142, so 4π² ≈ 39.478)

• L² = (4.5)² = 20.25
• t² = 5² = 25

g = 39.478 × (20.25 / 25) g = 39.478 × 0.81 g ≈ 31.98 ≈ 32.00 m/s²

Answer: Option C, 32.00 m/s².

Tip: When a formula has a square root, square both sides first. Then rearrange to isolate the unknown. Using π ≈ 3.14 gives about 31.9, which is still closest to 32.00, so the options are well separated.