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4. The period of a pendulum is 1.4 seconds. The length of the pendulum is increased by a factor of 4. What is the new period of the pendulum?
O A 0.7 seconds
OB. 1.4 seconds
O C.2.8 seconds
OD. 5.6 seconds

Respuesta :

Pipsqeak1

Answer:

C

Explanation:

The period of a pendulum is found by the equation: T = 2pi*sqrt(L/g). Let the original length be L and the original period be T. The length increased by a factor of 4, so it’s new length is 4L. We get that the new period is 2pi*sqrt(4L/g) = 2pi*2sqrt(L/g) = 4pi*sqrt(L/g). We can see that the period increased by a factor of 2 because the original period, T, equals 2pi*sqrt(L/g) and the new period is 4pi*sqrt(L/g) = 2(2pi*sqrt(L/g)) = 2T. Therefore, the new period is 2(1.4) = 2.8

I hope this helps! :)

Eduard22sly

The new period of the pendulum given that the length increased by a factor of 4 is 2.8 s

Formula for calculating period of pendulum

T = 2π√(L / g)

Where

  • T is the period
  • L is length
  • g is the acceleration due to gravity

How to determine the new period

  • Initial period (T₁) = 1.4 s
  • Initial length (L₁) = L
  • New length (L₂) = 4L
  • New period (T₂) =?

T = 2π√(L / g)

Square both side

T² = 4π²L / g

Divide both side by L

T² / L = 4π²/ g

Constant => 4π²/ g

T² / L = constant

Thus,

T²₁ / L₁ = T²₂ / L₂

1.4² / L = T²₂ / 4L

1.96 / L = T²₂ / 4L

Cancel out L

1.96  = T²₂ / 4

Cross multiply

T²₂ = 1.96 × 4

T²₂ = 7.84

Take the square root of both side

T₂ = √7.84

T₂ = 2.8 s

Learn more about period of simple pendulum:

https://brainly.com/question/14759840

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