A simple pendulum has a period of 1 s. The acceleration of gravity is 9.8 m/s2. How long is the pendulum?

Question

A simple pendulum has a period of 1 s.  The acceleration of gravity is 9.8 m/s2. How long is the pendulum?

BlackTom AI · Accepted Answer

Question restatement: A simple pendulum has a period of 1 s. The acceleration of gravity is 9.8 m/s^2. How long is the pendulum?

Options:
- 0.25 m
- 0.30 m
- 3.3 m
- 4.0 m

Step-by-step analysis:
- Start with the standard formula for a simple pendulum: T = 2π sqrt(L/g). This relates the period T to the length L and gravity g.
- Solve for L to compare with the given options: L = (g T^2) / (4π^2).
- Plug in the given values: g = 9.8 m/s^2 and T = 1 s.
  L = 9.8 * (1)^2 / (4 * π^2) ≈ 9.8 / 39.478...
  Numerically, 9.8 / 39.478 ≈ 0.248 m.
- Compare with each option:
  - 0.25 m: This is very close to the calculated 0.248 m, differing by about 0.002 m, which is within typical rounding tolerance in physics problems. This option is consistent with the formula and numbers.
  - 0.30 m: This would give a larger length, which would increase the period slightly beyond 1 s according to the formula; since the given period is exactly 1 s, 0.30 m is not supported by the calculation.
  - 3.3 m: This is orders of magnitude larger. If L were 3.3 m, the period T would be much longer than 1 s, contradicting the given data. The formula makes this clearly inconsistent.
  - 4.0 m: Similar to 3.3 m, a length of 4.0 m would yield a period far greater than 1 s, so this option does not fit the given information.
- Conceptual check: The period scales with the square root of length, so small changes in length produce smaller changes in T. The calculated L ≈ 0.248 m aligns with the tiny difference expected from rounding, reinforcing that the 0.25 m option is the physically correct choice.
- Summary: The mathematical result L ≈ 0.248 m supports the first option as the plausible length, while the other lengths lead to periods inconsistent with the given T = 1 s.

01:750:124 ANALYTICAL PHYSICS IB Module 8 Quiz 4 - Simple Harmonic Pendulum

A simple pendulum has a period of 1 s. The acceleration of gravity is 9.8 m/s2. How long is the pendulum?

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