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Chapter 2: Problem 6

The time period of a simple pendulum depends on its _

Short Answer

Expert verified
Answer: The time period of a simple pendulum depends on its length (L) and the acceleration due to gravity (g).

Step by step solution

01

Introduction: Simple Pendulum

A simple pendulum is a mass, called the bob, attached to a string or rod of fixed length. When the bob is pulled to one side and released, it swings back and forth in a motion called oscillation. The time it takes for the bob to complete one full oscillation is referred to as the time period of the pendulum.
02

Formula for Time Period

The time period (T) of a simple pendulum is determined by the following formula: T = 2π √(L/g) where L is the length of the pendulum and g is the acceleration due to gravity (approximately 9.81 m/s² on Earth).
03

Dependence on Length and Gravity

From the formula, we can see that the time period of a simple pendulum depends on two factors: the length of the pendulum (L) and the acceleration due to gravity (g). The longer the pendulum, the larger the time period, which means the pendulum takes longer to complete one oscillation. Meanwhile, a stronger gravitational pull leads to a shorter time period, as the pendulum oscillates more quickly.
04

Conclusion

In conclusion, the time period of a simple pendulum depends on its length and the acceleration due to gravity. By using the formula T = 2π √(L/g), we can calculate the time period for a specific pendulum in a given environment.

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Most popular questions from this chapter

Mention the different units of time and speed.

A simple pendulum of length ' \(\ell\) ' and time period ' \(\mathrm{T}\) ' on earth is taken onto the surface of moon. How should the length of the simple pendulum be changed on the moon such that the time period is constant. (Take \(\left.g_{e}=6 g_{i n}\right)\)

The speed of the tip of a second hand of length \(5 \mathrm{~cm}\) of a clock is \(\mathrm{m} \mathrm{s}^{-1}\) (1) 1 (2) 60 (3) \(5.3 \times 10^{-3}\) (4) \(3.4 \times 10^{-5}\)

The motion of molecules in a solid is an example for _ motion.

Match the entries given in column \(A\) with the appropriate ones in column \(\mathrm{B}\).
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