Topic: Dynamics
Concepts: Circular motion, Newton’s laws

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Solution:

Since the pendulum is undergoing circular motion, we have

so the tension is

At the bottom $\theta=0$, $\cos\theta$ is maximized since $\cos\,0=1$ while $v$ is also maximized by conservation of energy (pendulum is at lowest point of swing). Thus, both terms are maximized so the tension is largest at $\theta=0$. Hence, the answer is B.

Topic: Energy
Concepts: Circular motion, Conservation of energy

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Solution:

We found in the previous problem that the tension is maximized when the pendulum is at the bottom. We have

Since the pendulum amplitude is $\theta_0$, the pendulum has fallen a height

By conservation of energy,

Substituting this into the force equation,

so the answer is E.

Topic: Oscillatory Motion
Concepts: Dimensional analysis, Simple pendulum

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Solution:

By dimensional analysis, the period of a simple pendulum is given by

We are given

For the new pendulum of length $4L$ with the same amplitude $\theta_0$,

so the answer is A.