When a pendulum with a period of 2.00000 s is moved to a new location from one where the acceleration of gravity was 9.80 m/s2, its new period becomes 1.99711 s. By how much does the acceleration of gravity differ at its new location? (m/s2)

T=2πsqrt(L/g),

T₁=2πsqrt(L/g₁),

(T/T₁)²=g₁/g,
g₁ = g(T/T₁)² =…

9.816

To find the difference in acceleration of gravity at the two locations, we can use the equation for the period of a pendulum:

T = 2π√(L/g)

where T is the period, L is the length of the pendulum, and g is the acceleration of gravity.

Let's denote the acceleration of gravity at the initial location as g1 and the acceleration of gravity at the new location as g2.

Given that the period at the initial location (T1) is 2.00000 seconds and the period at the new location (T2) is 1.99711 seconds, we can set up the following equations:

T1 = 2π√(L/g1)
T2 = 2π√(L/g2)

Dividing the two equations to eliminate L:

T1/T2 = √(g2/g1)

Squaring both sides:

(T1/T2)^2 = g2/g1

Now let's substitute the given values:

(2.00000 / 1.99711)^2 = g2 / 9.80

Simplifying the left side:

(1.001445)^2 = g2 / 9.80

1.002891202025 = g2 / 9.80

To find g2, we'll multiply both sides by 9.80:

g2 = 9.80 * 1.002891202025

g2 ≈ 9.827 m/s^2

Therefore, the acceleration of gravity at the new location differs by approximately 9.827 - 9.80 = 0.027 m/s^2.

To find the difference in the acceleration of gravity at the new location, we can use the formula for the period of a pendulum:

T = 2π √(L/g)

where:
T is the period of the pendulum,
π is a mathematical constant approximately equal to 3.14159,
L is the length of the pendulum, and
g is the acceleration due to gravity.

In this case, we have two different periods (T1 and T2) and we need to find the difference in the acceleration due to gravity (Δg).

Let's assign the values given in the problem:
T1 = 2.00000 s (period at the first location)
T2 = 1.99711 s (period at the new location)
g1 = 9.80 m/s^2 (acceleration due to gravity at the first location)

Now we can set up two equations using the period formula, one for each location:

T1 = 2π √(L / g1)
T2 = 2π √(L / g2)

Since we have two equations with the same pendulum length (L), we can equate them:

2π √(L / g1) = 2π √(L / g2)

Simplifying the equation by canceling out the common terms:

√(L / g1) = √(L / g2)

Now we can square both sides of the equation to eliminate the square root:

L / g1 = L / g2

Cross-multiply the equation:

L * g2 = L * g1

Divide both sides of the equation by L:

g2 = g1

So, the acceleration due to gravity at the new location (g2) is equal to the acceleration due to gravity at the original location (g1) which is 9.80 m/s^2.

The difference in the acceleration of gravity at the new location is 0 m/s^2.