12 physics Activity: Second’s Pendulum Laws of Simple Pendulum.
Activity: Second’s Pendulum
Laws of Simple Pendulum.
⏱️ Activity: Second's Pendulum and Laws of Simple Pendulum (XII Science)
A simple pendulum consists of a point mass (bob) suspended by a light, inextensible string from a rigid support. When displaced from its equilibrium position, it performs simple harmonic motion (SHM).
🎯 Aim
To determine the acceleration due to gravity (g) using a simple pendulum.
To verify the Laws of Simple Pendulum.
To determine the length of a Second's Pendulum at the place of experiment.
💡 Theory and Laws of Simple Pendulum
The time period (T) of a simple pendulum is the time taken to complete one full oscillation. For small angular displacements, the time period is given by the formula:
where:
Tis the time period (in seconds).
Lis the effective length of the pendulum (length of string + radius of the bob, in meters).
g is the acceleration due to gravity
By squaring both sides, we can derive the formula for g:
Diagram
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A Second's Pendulum is defined as a simple pendulum whose time period is 2 seconds (i.e., it takes 1 second to swing from one extreme to the other). Its length Ls is found by setting T=2 s in the main formula:
Law of Length: The time period (T) is directly proportional to the square root of the effective length (L), provided g and (amplitude) are constant.
Law of Mass: The time period (T) is independent of the mass or material of the bob, provided L, g, and amplitude are constant.
Law of Amplitude: The time period (T) is independent of the amplitude (theta), provided the amplitude is small (less than about 10 degree).
Law of Acceleration due to Gravity: The time period (T) is inversely proportional to the square root of the acceleration due to gravity (g) at the place of experiment, provided L and theta are constant. .
🛠️ Procedure (Outline)
Suspend the bob with the thread from a rigid support and accurately measure the effective length $L$ (length of string from the support to the center of the bob) using a meter scale.
Displace the bob through a small angle (not more than 10degree) and release it.
Start the stopwatch when the bob passes through the mean position in one direction.
Count and record the time (t) taken for 20 complete oscillations.
Calculate the time period T = t / 20.
Repeat the measurement of T for at least four different lengths of the pendulum (e.g., L = 120 cm, 110cm, 100 cm, 90 cm.
Plot a graph between L and T^2 (Verification of the Law of Length).
📋 Observations and Tabulation
| S.No. | Length of string l (cm) | Radius of bob r (cm) | Effective Length L=l+r (m) | Time for 20 oscillations t (s) | Time Period T=t/20 (s) | T2 (s2) | L/T2 (m/s2) |
| 1 | 118.0 | 2.0 | 1.200 | 39.2 | 1.960 | 3.8416 | 0.3124 |
| 2 | 108.0 | 2.0 | 1.100 | 37.3 | 1.865 | 3.4782 | 0.3162 |
| 3 | 98.0 | 2.0 | 1.000 | 35.8 | 1.790 | 3.2041 | 0.3121 |
| 4 | 88.0 | 2.0 | 0.900 | 33.8 | 1.690 | 2.8561 | 0.3151 |
| 5 | (Second's Pendulum) | 2.0 | Ls | 40.0 | 2.000 | 4.0000 | 0.25 |
(Sample readings are provided above)
🔢 Calculations
A. Calculation of Acceleration due to Gravity (g)
The acceleration due to gravity g is calculated using the formula
✅ Result
The acceleration due to gravity (g) at the place of experiment is12.385m/s2
The length of the Second's Pendulum (Ls) is 1.255 m.
1. A second’s pendulum has a time period of:
A. 1 s
B. 2 s
C. 4 s
D. 0.5 s
✔ Answer: B
2. The length of a second’s pendulum on Earth is approximately:
A. 25 cm
B. 50 cm
C. 100 cm
D. 200 cm
✔ Answer: C
3. The time period of a simple pendulum depends on:
A. Mass of the bob
B. Shape of the bob
C. Length of the pendulum
D. Material of the bob
✔ Answer: C
4. The law of simple pendulum states that time period is proportional to:
A. Mass of bob
B. Amplitude
C. Square root of length
D. Length
✔ Answer: C
5. The time period of a simple pendulum is independent of:
A. Length
B. Acceleration due to gravity
C. Amplitude (small oscillations)
D. Mass of the bob
✔ Answer: D
6. If the length of a pendulum is made four times, its time period becomes:
A. Double
B. Half
C. Four times
D. One-fourth
✔ Answer: A
7. If the acceleration due to gravity increases, the time period of a simple pendulum will:
A. Increase
B. Decrease
C. Remain unchanged
D. Become zero
✔ Answer: B (Decrease)
8. The time period of a pendulum increases when:
A. Mass increases
B. Length increases
C. Amplitude decreases
D. Bob is changed
✔ Answer: B
9. A simple pendulum will not show SHM if:
A. Length is large
B. Amplitude is small
C. Amplitude is large
D. Mass is small
✔ Answer: C
10. The acceleration due to gravity at a place can be determined using:
A. Spring balance
B. Simple pendulum
C. Bar magnet
D. Voltmeter
✔ Answer: B
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