A simple pendulum of length l has a period of oscillation of 2.0\text{ s} when suspended w… — JAMB UTME

A simple pendulum of length $l$ has a period of oscillation of $2.0\text{ s}$ when suspended with a bob of mass $50\text{ g}$ . If the bob is replaced with one of mass $200\text{ g}$ while maintaining the exact same string length, what is the new period of oscillation?

$2.0\text{ s}$ Answer
B
$4.0\text{ s}$
C
$1.0\text{ s}$
D
$8.0\text{ s}$

Answer

The period of oscillation remains

2.0\text{ s}

The period of oscillation of a simple pendulum undergoing simple harmonic motion is given by

T = 2\pi \sqrt{\frac{l}{g}}

, where

l

is the length of the pendulum and

g

is the acceleration due to gravity. Because the mass of the bob does not appear in this equation, changing the mass from

50\text{ g}

200\text{ g}

does not alter the period. Therefore, the period remains

2.0\text{ s}

Step-by-Step Solution

Identify the formula for the period of a simple pendulum.

T = 2\pi \sqrt{\frac{l}{g}}

The period

T

depends on the length of the pendulum

l

and local acceleration due to gravity

g

Analyze the dependence of period on bob mass.

The mass parameter

m

does not appear in the formula

T = 2\pi \sqrt{\frac{l}{g}}

The period of a simple pendulum is independent of the mass of the bob.

Determine the new period of oscillation.

T_{new} = 2.0\text{ s}

Since length

l

and acceleration due to gravity

g

remain unchanged, the period stays

2.0\text{ s}

Key Concept

Independence of simple pendulum period from bob mass

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