Simple Pendulum

Question

A grandfather clock keeps time using a simple pendulum, and its bob swings with a period of exactly 2 s at a place where g equals 9.8 m per second squared. What is the approximate length of this pendulum?

RankGuru · Accepted Answer

A simple pendulum oscillating through small angles behaves as an SHM system with period $T = 2\pi\sqrt{L/g}$, where $L$ is the length and $g$ is the gravitational acceleration. The restoring agent here is the tangential component of gravity, which for small angles is proportional to displacement. Solving for length gives $L = \frac{gT^2}{4\pi^2}$. Substituting $T = 2	ext{ s}$ and $g = 9.8	ext{ m/s}^2$, we get $L = \frac{9.8 	imes 4}{4\pi^2} = \frac{39.2}{39.48} \approx 0.99	ext{ m}$. The value $0.50	ext{ m}$ wrongly uses $T = 1	ext{ s}$ or halves the result. The value $2.00	ext{ m}$ simply copies the period as if it were a length, which is dimensionally invalid. The value $1.96	ext{ m}$ omits the $4\pi^2$ denominator and instead divides only by 4. This is the classic seconds-pendulum result discussed in NCERT oscillations. As a plausibility check, a seconds pendulum is historically known to be about one metre long, confirming that $0.99	ext{ m}$ is the physically expected answer.

Simple Pendulum

Select the correct option:

🔒 Solution Hidden from View

More oscillations and waves Practice Questions

A pendulum clock keeps correct time on Earth, but if it were taken to the Moon where gravity is abou...

A simple pendulum used to determine acceleration due to gravity has a measured length of 1.0 m and a...

In the simple pendulum experiment for g, a student wants to reduce the fractional error in the resul...

Approximate length of simple pendulum with period 2 s (g=10 m/s²)?

Comparing uniform circular motion with simple harmonic motion, the projection of a particle moving s...

Sound propagating through the air inside a long tube compresses and rarefies the medium along the di...

A stretched guitar string carries a tension of 80 N and has a linear mass density of 0.005 kg per me...

According to the Laplace correction, the speed of sound in a gas depends on which combination of gas...

Two waves of the same frequency travelling in a medium arrive at a point exactly out of phase with e...

A string fixed at both ends and one metre long vibrates in its fundamental mode, so what is the wave...

An organ pipe closed at one end and open at the other resonates in its lowest mode, so which harmoni...

A piano tuner sounds a reference fork of 256 hertz alongside a slightly mistuned string and hears fo...

About This Question

Solution