Pendulum Period Calculation

The question asks us to find the period of a simple pendulum with a given length, using a standard formula and specific values for gravity and pi. We need to calculate the period and round the result to the first decimal place.

Pendulum Formula

The formula provided for the period ($T$) of a simple pendulum is:

$\text{T} = 2 \pi \sqrt{\frac{\text{l}}{\text{g}}}$

Where:

• $\text{T}$ is the period of the pendulum (in seconds)
• $\pi$ is a mathematical constant
• $\text{l}$ is the length of the pendulum (in meters)
• $\text{g}$ is the acceleration due to gravity (in m/s²)

Given Values

We are given the following values:

• Length of the pendulum, $\text{l} = 1 \text{ m}$
• Acceleration due to gravity, $\text{g} = 9.81 \text{ m/s}^2$
• Value of pi, $\pi = 3.1416$

Calculating the Pendulum Period

Now, we substitute the given values into the formula for the period:

$\text{T} = 2 \times 3.1416 \times \sqrt{\frac{1}{9.81}}$

First, calculate the value inside the square root:

$\frac{1}{9.81} \approx 0.1019368$

Next, calculate the square root of this value:

$\sqrt{0.1019368} \approx 0.319275$

Now, multiply the terms together:

$\text{T} = 2 \times 3.1416 \times 0.319275$

$\text{T} = 6.2832 \times 0.319275$

$\text{T} \approx 2.00581$ seconds

Rounding the Period

The question asks for the period correct to the first place of decimal. Our calculated value is approximately $2.00581$.

To round to the first decimal place, we look at the second decimal digit. If it is 5 or greater, we round up the first decimal digit. If it is less than 5, we keep the first decimal digit as it is.

In $2.00581$, the first decimal digit is 0, and the second decimal digit is 0. Since 0 is less than 5, we keep the first decimal digit as 0.

So, $2.00581$ rounded to the first decimal place is $2.0$.

Final Answer

The period of the pendulum of length 1 m, correct to the first place of decimal, is 2.0 seconds.

The calculated period of the pendulum, rounded to one decimal place, matches one of the provided options.