Answer:
8.91 %
Explanation:
Since v² = 2gy
By the relative error formula,
2Δv/v = Δg/g + Δy/y multiplying by 100%, we have
2Δv/v × 100% = Δg/g × 100 % + Δy/y × 100%
2(Δv/v × 100%) = Δg/g × 100 % + Δy/y × 100%
Δg/g × 100 % = 2(Δv/v × 100%) - Δy/y × 100%
Since Δv/v × 100% = 3.69 % and Δy/y × 100% = 5 %
Since we have a difference for the percentage error in g, we square the percentage errors and add them together. So,
[Δg/g × 100 %]² = [2(Δv/v × 100%)]² + [Δy/y × 100%]²
[Δg/g × 100 %]² = [2(3.69)]² + [5%]²
[Δg/g × 100 %]² = [4)(3.69 %)² + [5%]²
[Δg/g × 100 %]² = 54.4644 %² + 25%²
[Δg/g × 100 %]² = 79.4644 %²
taking square-root of both sides, we have
[Δg/g × 100 %] = 8.91 %
So, the percent uncertainty in the calculated value of g is 8.91 %
