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

Acceleration due to gravity on Mars = 3.72 m/s²

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.