The period of a simple pendulum is 8 s. If the same pendulum experiment is repeated on a plant of g = 1/4 gE, the new period is

16 secs.

Explanation:

Data obtained from the question include the following:

Period on earth (T) = 8 secs

Next period (Tn) =?

Next, we shall determine the length of the string. This can be obtained as follow:

Period on earth (T) = 8 secs

Acceleration due to gravity on earth (gE) = 9.8 m/s²

Pi (π) = 3.14

Length of string (L) =?

T = 2π√(L/gE)

8 = 2 × 3.14 ×√(L/9.8)

8 = 6.28 × √(L/9.8)

Divide both side by 6.28

8/6.28 = √(L/9.8)

Take the square of both side

(8/6.28)² = L/9.8

Cross multiply

L = (8/6.28)² × 9.8

L = 15.9 m

Therefore the length of string is 15.9 m

Next, we shall determine the new period of the pendulum as follow:

Length (L) = constant = 15.9 m

Pi (π) = 3.14

Acceleration due to gravity on earth (gE) = 9.8 m/s²

Acceleration due to gravity on the planet (g) = 1/4 gE = 1/4 × 9.8 m/s²

= 2.45 m/s²

New period (Tn) =?

Tn = 2π√(L/g)

Tn = 2 × 3.14 × √(15.9/2.45)

Tn = 6.28 × √(15.9/2.45)

Tn = 16 secs.

Therefore, the new period of the pendulum is 16 secs.

they should be similar or the same

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