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12. A simple pendulum is put into oscillation on Earth, Pluto, Mars and Jupiter....

Jan 29, 2024

12. A simple pendulum is put into oscillation on Earth, Pluto, Mars and Jupiter. Given that their gravitational accelerations are

10 \mathrm{~ms}^{-2}, 0.8 \mathrm{~ms}^{-2}, 3.8 \mathrm{~ms}^{-2}

, and

25.4 \mathrm{~ms}^{-2}

respectively, on which celestial body will the simple pendulum oscillate the fastest? A Earth B Pluto C Mars D Jupiter

Solution by Steps

step 2

The period

T

is inversely proportional to the square root of the gravitational acceleration

g

. Therefore, the larger the value of

g

, the smaller the period

T

, meaning the pendulum oscillates faster

step 3

We compare the given gravitational accelerations: Earth (

10 \mathrm{~ms}^{-2}

), Pluto (

0.8 \mathrm{~ms}^{-2}

), Mars (

3.8 \mathrm{~ms}^{-2}

), and Jupiter (

25.4 \mathrm{~ms}^{-2}

)

step 4

Since Jupiter has the highest gravitational acceleration (

25.4 \mathrm{~ms}^{-2}

), the pendulum will oscillate the fastest on Jupiter

Key Concept

Gravitational Acceleration and Pendulum Period

Explanation

The period of a simple pendulum is inversely proportional to the square root of the gravitational acceleration. The higher the gravitational acceleration, the faster the pendulum oscillates.