Question

2. One of two identical grandfather pendulum clocks from Earth is placed on Mars. If the grandfather clock on Mars is 23 minutes behind the grandfather clock on Earth after 1 hour, what is the acceleration due to gravity on Mars

Answer 1

To determine the acceleration due to gravity on Mars, we can compare the periods of the grandfather pendulum clocks on Earth and Mars. Using the equation for the period of a pendulum, we can express the acceleration due to gravity on Mars in terms of the length and period of the pendulum.

Step-by-step explanation:

To determine the acceleration due to gravity on Mars, we can use the relationship between the period of a pendulum and the acceleration due to gravity. The period T of a pendulum is given by the equation T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity.

Since the two grandfather pendulum clocks are identical, we can equate their periods: TEarth = TMars. After substituting the values of the period and length, we can solve for gMars by rearranging the equation: gMars = (L/TMars)² * 4π².

Using the given values, we can find:

gMars = (L/23)^2 * 4π².

Answer 2

Acceleration due to gravity on Mars = 3.72 m/s²

Step-by-step explanation:

It is given that the grandfather clock on Mars lags 23 minutes behind the grandfather clock on Earth after 1 hour.

Mars = 60 - 23 = 37 minutes

So the time on Mars is 37 minutes when time on Earth is 60 minutes.

We know that time period on Earth is given by

Te = 2π√(L/ge)

Where ge is acceleration due to gravity on the Earth

We know that time period on Mars is given by

Tm = 2π√(L/gm)

Where gm is acceleration due to gravity on the Mars

So,

Te/Tm = 37/60 = 0.616

0.616 = 2π√(L/ge)/2π√(L/gm)

Simplifying the above equation yields

0.616 = √gm/√ge

√gm = √ge*0.616

squaring on both sides

gm = ge*0.616²

The acceleration on the Earth is 9.81 m/s²

gm = 9.81*0.616²

gm = 3.72 m/s²

Therefore, the acceleration due to gravity on Mars is 3.72 m/s².