Question

Savitha notes down the data of time taken to complete 30 oscillations as 60 s and hence calculates the length of the simple pendulum as: (Take $\pi^2 = 9.8$, and $g = 9.8$ m/s$^2$)

• A. 2 m
• B. 1 m
• C. 0.75 m
• D. 1.5 m

Hint:

A pendulum with a time period of exactly 2 seconds is called a "Seconds Pendulum." Its length is always approximately 1 meter on Earth.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The time period ($T$) of a simple pendulum is the time taken for one complete oscillation. It is related to the length ($L$) and acceleration due to gravity ($g$).

Step 2: Key Formula or Approach:
1. $T = \frac{\text{Total Time}}{\text{Number of Oscillations}}$ 2. $T = 2\pi\sqrt{\frac{L}{g}}$

Step 3: Detailed Explanation:
1. Find Time Period ($T$): \[ T = \frac{60 \text{ s}}{30 \text{ oscillations}} = 2 \text{ s} \] 2. Rearrange the Period formula for $L$: \[ T^2 = 4\pi^2 \frac{L}{g} \implies L = \frac{T^2 g}{4\pi^2} \] 3. Substitute the values: - $T = 2$ - $g = 9.8$ - $\pi^2 = 9.8$ \[ L = \frac{(2)^2 \times 9.8}{4 \times 9.8} \] \[ L = \frac{4 \times 9.8}{4 \times 9.8} = 1 \text{ m} \]

Step 4: Final Answer:
The length of the simple pendulum is 1 m.