if the length of a pendulum increases, the period of the pendulum?

Answer 1

increases?

Answer 2

For a simple pendulum,

ω = √((mgL)/ I), where ω = rotational velocity, m = mass of pendulum, g = acceleration due to gravity, L = length of pendulum, and I = moment of inertia.

Now, for the simple pendulum I = mr² and r in this case is L so I = mL².

So, substitute I into the ω equation.

ω = √((mgL)/ I) = √((mgL) / (mL²)) = √(g/L).

So, if L is increased; therefore, ω will decrease. Well ω = 2π / T, so with a decrease in ω; therefore, T (period) will increase.

In summary, if L (length) is increased, then T (period) will increase.

Answer 3

Increases. The period of a simple pendulum, when the swing amplitude is small, is
T = 2*pi*sqrt(L/g)

Answer 4

T = 2pi square^1/2 (l/g).

Then, if the length increases, the period increases too, but not with a linear relationship.