To Study a Simple Pendulum and Find the Acceleration Due to Gravity (g) (Class 10 Physics Practical)
To determine the value of g using a simple pendulum by studying the relationship between time period and length.
TL;DR: To determine the value of g using a simple pendulum by studying the relationship between time period and length.
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
Aim: To determine the value of g using a simple pendulum by studying the relationship between time period and length.
Materials Required
- Simple pendulum setup
- Meter scale
- Stopwatch
- Bob (weight)
- String
- Clamp and stand
- Protractor
Theory
The time period T of a simple pendulum is given by T = 2π√(L/g), where L is length and g is acceleration due to gravity. By measuring the time period for different lengths, a graph of T² vs L is plotted. The slope equals 4π²/g, from which g can be calculated.
Procedure
- Set up a simple pendulum by suspending a bob with a string from a fixed point
- Measure the length L of the pendulum from the point of suspension to the center of the bob
- Displace the bob by a small angle (less than 15 degrees) and release it
- Measure the time for 20 oscillations using a stopwatch
- Calculate the time period: T = Time for 20 oscillations / 20
- Repeat for 6-7 different lengths from 30 cm to 100 cm
- Plot a graph of T² (y-axis) vs L (x-axis); it should be a straight line through origin
- Calculate slope = 4π²/g; therefore g = 4π²/slope
Observation
For L = 25 cm, T ≈ 1.0 second. For L = 100 cm, T ≈ 2.0 seconds. The relationship shows that time period increases with increasing length. The T² vs L graph is linear, confirming the theoretical relationship.
Result
The value of g is determined to be approximately [value] m/s², which is close to the standard value of 9.8 m/s² at Earth's surface.
Precautions
- Ensure the suspension point is fixed and rigid
- Measure length from the point of suspension to the center of the bob
- Use small amplitude oscillations (less than 15 degrees)
- Measure time for multiple oscillations to reduce error
- Perform readings at least 3 times for each length and take average
- Ensure the bob does not collide with obstacles
Viva Questions
What is the formula for the time period of a simple pendulum?
T = 2π√(L/g), where L is length and g is acceleration due to gravity.
Why should the amplitude of oscillation be small?
For small amplitudes, the pendulum behaves as a simple harmonic oscillator and the formula is valid. Large amplitudes make the period dependent on amplitude.
What is the relationship between T² and L?
T² is directly proportional to L. The graph of T² vs L is linear with slope = 4π²/g.
Why do we plot T² vs L instead of T vs L?
Plotting T² vs L gives a linear graph, making it easier to find g from the slope.
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