Answer:
the clock will only read 4.9 min on Earth
Explanation:
This watch can be approximated by a simple pendulum that is a rope with a point mass at its end, the angular speed is
w = √ g / L
angular velocity is related to frequency and is to period
w = 2π f = 2π / T
T = 2π √L /g
let's analyze the situation on the moon,
T = 2π √(1 / 1,62)
T = 4.937 s
this indicates that each oscillation corresponds to the time T when the clock has advanced 12 minutes, we can find how many rotten it has made
Let's start by reducing the time to the SI system
t = 12 min (60s / 1 min) = 720 s
now let's use a direct ratio. If one oscillation in T how many oscillations in t
#_oscillation = t / T
#_oscillation = 720 / 4,937
# _oscillation = 145.8
Let's see how long the same pendulum has on Earth when it gives this number of oscillations
T_earth = 2π √ L / g
T_earth = 2π √(1 / 9.8)
T _earth = 2.01 s
Now we can know the time it uses in the 145.8 oscillations
t = #_ oscillations T_earth
t = 145.8 2.01
t = 292.63 s
let's reduce to minutes
t = 292.63 s (1min / 60s) = 4.88 min
therefore the clock will only read 4.9 min on Earth