On an unknown planet, a pendulum of length 1.5 m swings with a period of 3.3 s. What is the acceleration of gravity on this planet?
T = 2 pi sqrt (L/g)
3.3 = 2 pi sqrt (1.5/g)
sqrt(1.5/g)= .5252
1.5/g = .276
g = 5.44 m/s^2 around half earth g
To find the acceleration of gravity on the unknown planet, we can use the equation for the period of a simple pendulum:
T = 2π √(L/g)
where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
Rearranging the equation to solve for g, we get:
g = (4π²L) / T²
Now we can substitute the given values:
Length of the pendulum, L = 1.5 m
Period of the pendulum, T = 3.3 s
Plugging in these values, we have:
g = (4π² * 1.5) / (3.3^2)
Calculating this expression yields:
g ≈ 9.96 m/s²
Therefore, the acceleration of gravity on this unknown planet is approximately 9.96 m/s².
To find the acceleration of gravity on the unknown planet, we can make use of the formula for the period of a pendulum:
T = 2π√(L/g)
Where:
T is the period of the pendulum,
L is the length of the pendulum,
g is the acceleration due to gravity.
In this case, we are given that the length of the pendulum, L, is 1.5 m and the period, T, is 3.3 s. We need to solve for the acceleration due to gravity, g.
Rearranging the formula, we get:
g = (4π²L) / T²
Now we can substitute the given values into the equation:
g = (4π² * 1.5) / (3.3²)
Calculating this expression gives us the value of acceleration due to gravity on the unknown planet.