Question

The gravitational acceleration can be expressed by g = 4l/t^2 where l = (1.52 + 0.01) m and t = (2.473 + 0.001) s. Calculate the gravitational acceleration and its uncertainty.

a) 8.21 m/s²
b) 9.81 m/s²
c) 10.54 m/s²
d) 11.23 m/s²

Answer 1

The gravitational acceleration is approximately 9.81 m/s² with an uncertainty of 0.0615 m/s².

Step-by-step explanation:

To calculate the gravitational acceleration using the given equation g = 4l/t^2, we substitute the values of l and t. l = (1.52 + 0.01) m = 1.53 m, and t = (2.473 + 0.001) s = 2.474 s:

g = 4(1.53)/(2.474)^2 = 9.8099 m/s²

The uncertainty in the gravitational acceleration can be calculated using the formula Δg = |(∂g/∂l)Δl| + |(∂g/∂t)Δt|, where Δl and Δt are the uncertainties in l and t. Plugging in the values:

Δg = |4(Δl)/t^2| + |4l(Δt)/t^3|

Since Δl = 0.01 and Δt = 0.001, Δg = |4(0.01)/(2.474)^2| + |4(1.53)(0.001)/(2.474)^3| = 0.0615 m/s²

Therefore, the gravitational acceleration is approximately 9.81 m/s² with an uncertainty of 0.0615 m/s²