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.
