In a simple pendulum experiment , the length of the pendulum is 90.6*10^-2 m the time period s 1.91 second.write the value of acceleration due to gravity to correct significant figures and round it of?

Question

Answer

Calculating Acceleration due to Gravity in a Simple Pendulum Experiment

Given Information:

Length of the pendulum (l) = 90.6*10^-2 m

Time period (T) = 1.91 seconds

Formula Used:

The time period of a simple pendulum is given by the formula T = 2π √(l/g), where 'g' is the acceleration due to gravity.

Calculation:

Using the formula T = 2π √(l/g), we can rearrange it to find 'g' as follows:

g = (4π^2 l) / T^2

Substituting the given values, we get:

g = (4π^2 * 90.6*10^-2) / (1.91)^2

g = 9.79 m/s^2 (rounded off to two decimal places)

Explanation:

In a simple pendulum experiment, the time period (T) is the time taken for one complete oscillation, i.e., the time taken for the bob to move from one extreme position to the other and back. The time period depends on the length of the pendulum (l) and the acceleration due to gravity (g). The formula T = 2π √(l/g) relates these variables.

To find the acceleration due to gravity, we can rearrange the formula as g = (4π^2 l) / T^2. By substituting the given values of T and l, we can calculate 'g' to be 9.79 m/s^2.

It is important to round off the answer to the correct number of significant figures. In this case, we have two significant figures in the given values (90.6 and 1.91), so we must round off the answer to two significant figures as well. Therefore, the final answer is 9.79 m/s^2.

Overall, the simple pendulum experiment is a useful tool for measuring the acceleration due to gravity, which has a value of approximately 9.81 m/s^2 at sea level. However, this value may vary slightly depending on the location and other factors.

Answer

As T=2pie*underroot L/g

So g=4*pie^2*L/T^2

Put the values

g=4*3.14*3.14*90.6*10^-2/1.91*1.91

=3573.120*10^-2/3.6481

=979.447*10^-2

=9.81 m/s

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