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?

查看解析

登录即可查看完整答案

类似问题

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

People born without creativity never can develop it

A product has a selling price of $20, a contribution margin ratio of 40% and fixed cost of $120,000. To make a profit of $30,000. The number of units that must be sold is: Type the number without $ and a comma. Eg: 20000

Which of the following statement regarding cost is correct:

Under the assumptions used in cost-volume-profit analysis, as the activity increases:

The CVP and break-even analysis are supported by a range of important assumptions. Which of the following is not an assumption of the CVP:

The break-even point is that at which:

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单