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

Answer:

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.