Acceleration due to Gravity (g) using Simple Pendulum
What you will learn
Determine acceleration due to gravity (g) at a place by studying the variation of time period (T) with effective length (L) of a simple pendulum and plotting an L-T² graph.
Materials needed
- Heavy Metallic Bob with small hook (brass)What is it?Heavy Metallic Bob with small hook (brass)₹50
Solid machined brass spherical pendulum bob with integral brass suspension ring.
Specifications- Mass
- 150 grams
- Diameter
- 25.0 mm
- Material
- High density naval brass
- Finish
- Polished lacquer coat
- Fine unspun cotton thread (appro.5 m)What is it?Fine unspun cotton thread (appro.5 m)₹95
Cast iron laboratory retort stand with 75 cm steel rod and heavy rectangular base.
Specifications- Base Size
- 200 mm × 125 mm × 25 mm
- Rod Dimensions
- 750 mm length, 12.5 mm diameter
- Weight
- 2.5 kg stability base
- Clamp
- Universal bosshead and jaw clamp
- Split Cork & Rigid Retort Stand with clampWhat is it?Split Cork & Rigid Retort Stand with clamp₹140
Unspun fine linen suspension thread and split cork pad.
Specifications- Thread Type
- Inextensible waxed linen cord
- Length
- 1.5 meters
- Cork
- Natural split cork stopper
- Tensile Strength
- 5 kg proof
- Precision Vernier Caliper for measuring bob radiusWhat is it?Precision Vernier Caliper for measuring bob radius₹185
Precision digital quartz stopwatch with lap memory and split counting.
Specifications- Resolution
- 0.01 second (10 ms)
- Accuracy
- ± 0.001 s/day
- Display
- High contrast 7-digit LCD
- Controls
- Start, Stop, Split/Reset
- Digital Stopwatch (least count 0.01s)What is it?Digital Stopwatch (least count 0.01s)₹230
Standard laboratory apparatus used in Acceleration due to Gravity (g) using Simple Pendulum.
Specifications- Category
- Physics Apparatus
- Grade
- CBSE / NEP 2020 Laboratory Standard
- Meter Scale & Chalk for fiducial markWhat is it?Meter Scale & Chalk for fiducial mark₹275
Standard laboratory apparatus used in Acceleration due to Gravity (g) using Simple Pendulum.
Specifications- Category
- Physics Apparatus
- Grade
- CBSE / NEP 2020 Laboratory Standard
Tick items as you collect them. Tap + to see the product, specifications and buy options.
Stay safe
- Angular amplitude of oscillation must be kept very small (< 4°-5°) for true SHM behavior (sin θ ≈ θ).
- The pendulum must oscillate strictly in a single vertical plane without spinning.
- Ensure the suspension point is rigid and does not yield during oscillations.
- Air currents must be prevented by shutting nearby fans and windows.
Steps
- 1Measure the diameter of the brass bob with a Vernier caliper in two perpendicular directions and compute its radius r.Observation
Measure bob diameter with Vernier Caliper (2r = 2.50 cm => r = 1.25 cm); add to thread length for effective length L.
SafetyTighten split cork securely in retort clamp so thread suspension point does not slip.
- 2Tie one end of the fine thread to the hook of the bob and pass the other end through the split cork held firmly in the clamp.Observation
Mark equilibrium reference line with chalk on bench floor directly behind suspended bob.
SafetyEnsure heavy retort stand base is stabilized with a counterweight.
- 3Adjust the thread length such that the effective length L (length of thread + hook + bob radius) is exactly 70 cm.Observation
Displace bob horizontally by no more than 3 to 4 cm (angular displacement < 4°) for simple harmonic motion.
SafetyRelease bob gently without imparting any spin, twist, or elliptical trajectory.
- 4Make a vertical chalk mark on the wall behind the bob's rest position as the reference mean position.Observation
Start digital stopwatch as bob crosses central equilibrium line; count 20 full return oscillations.
SafetyTurn off ceiling fans to prevent turbulent air drag on oscillating bob.
- 5Displace the bob slightly (amplitude < 5°) and release it without jerk to execute simple harmonic motion.Observation
Record t = 35.9 s for L = 0.80 m; average across three trials gives T = 1.795 s.
SafetyReset stopwatch smoothly after recording time.
- 6Using the stopwatch, time 20 complete oscillations and calculate the time period T = time / 20.Observation
Graph L vs T² yields slope 0.248 m/s²; multiplying by 4π² gives g = 9.80 m/s².
SafetyStore brass bob safely in storage drawer to prevent floor damage.
- 7Repeat for lengths 80 cm, 90 cm, 100 cm, 110 cm, and 120 cm, then plot the L versus T² graph.
Tap + on a step to see what you will observe and any safety tips.
Record your observations
| Length of Pendulum L (m) | Time for 20 Oscillations t (s) | Time Period T = t/20 (s) | T² (s²) | Calculated g = 4π²L/T² (m/s²) |
|---|---|---|---|---|
| 0.60 m | 31.0 s | 1.55 s | 2.40 s² | 9.87 m/s² |
| 0.70 m | 33.6 s | 1.68 s | 2.82 s² | 9.79 m/s² |
| 0.80 m | 35.9 s | 1.80 s | 3.24 s² | 9.75 m/s² |
| 0.90 m | 38.1 s | 1.90 s | 3.61 s² | 9.83 m/s² |
| 1.00 m | 40.1 s | 2.00 s | 4.00 s² | 9.87 m/s² |
Tap a highlighted cell to write your own observation.
Result and conclusion
The L-T² graph is a linear straight line passing through the origin. The acceleration due to gravity g is calculated as 9.78 m/s² ± 0.05 m/s².
| Observation | What it means |
|---|---|
| Isochronism Verified | Time period depends solely on length L and gravitational field g; independent of bob mass or small amplitude (< 5°). |
| L vs T² Linearity | The plot of L versus T² is a straight line through origin with slope L/T² = 0.248 m/s². |
| Accurate Local Value of g | Mean calculated g = 9.80 ± 0.04 m/s², matching standard Earth sea-level gravitational acceleration. |
| Effective Length Inclusion | Accurately adding the hook length and bob spherical radius (r = 1.25 cm) removes systematic zero offset. |
Sample readings. Replace with your own results.