Answer:
g' = 0.31 m/s²
Explanation:
First we need to find the length of pendulum, by using the formula of the time period of pendulum:
T = 2π√(L/g)
L = T²g/4π²
where,
L = Length of Pendulum = ?
T = Time Period of Pendulum on Earth = 2 s
g = acceleration due to gravity on Earth = 9.8 m/s²
Therefore,
L = (2 s)²(9.8 m/s²)/4π²
L = 0.99 m
Now, we use the formula on asteroid:
T' = 2π√(L/g')
where,
T' = Time Period on Asteroid = 11.3 s
g' = acceleration due to gravity on asteroid = ?
Therefore,
11.3 s = 2π √(0.99 m/g')
(11.3 s)² = 4π²(0.99 m/g')
g' = 39.2 m/(11.3 s)²
g' = 0.31 m/s²
