The new period is D) √2 T
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
<h3>Further explanation</h3>
Let's recall Elastic Potential Energy and Period of Simple Pendulum formula as follows:
![\boxed{E_p = \frac{1}{2}k x^2}](https://tex.z-dn.net/?f=%5Cboxed%7BE_p%20%3D%20%5Cfrac%7B1%7D%7B2%7Dk%20x%5E2%7D)
where:
<em>Ep = elastic potential energy ( J )</em>
<em>k = spring constant ( N/m )</em>
<em>x = spring extension ( compression ) ( m )</em>
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
![\boxed{T = 2\pi \sqrt{ \frac{L}{g} }}](https://tex.z-dn.net/?f=%5Cboxed%7BT%20%3D%202%5Cpi%20%5Csqrt%7B%20%5Cfrac%7BL%7D%7Bg%7D%20%7D%7D)
where:
<em>T = period of simple pendulum ( s )</em>
<em>L = length of pendulum ( m )</em>
<em>g = gravitational acceleration ( m/s² )</em>
Let us now tackle the problem!
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
<u>Given:</u>
initial length of pendulum = L₁ = L
initial mass = M₁ = M
final length of pendulum = L₂ = 2L
final mass = M₂ = 2M
initial period = T₁ = T
<u>Asked:</u>
final period = T₂ = ?
<u>Solution:</u>
![T_1 : T_2 = 2\pi \sqrt{ \frac{L_1}{g} }} : 2\pi \sqrt{ \frac{L_2}{g} }}](https://tex.z-dn.net/?f=T_1%20%3A%20T_2%20%3D%202%5Cpi%20%5Csqrt%7B%20%5Cfrac%7BL_1%7D%7Bg%7D%20%7D%7D%20%3A%202%5Cpi%20%5Csqrt%7B%20%5Cfrac%7BL_2%7D%7Bg%7D%20%7D%7D)
![T_1 : T_2 = \sqrt{L_1} : \sqrt{L_2}](https://tex.z-dn.net/?f=T_1%20%3A%20T_2%20%3D%20%5Csqrt%7BL_1%7D%20%3A%20%5Csqrt%7BL_2%7D)
![T : T_2 = \sqrt{L} : \sqrt{2L}](https://tex.z-dn.net/?f=T%20%3A%20T_2%20%3D%20%5Csqrt%7BL%7D%20%3A%20%5Csqrt%7B2L%7D)
![T : T_2 = 1 : \sqrt{2}](https://tex.z-dn.net/?f=T%20%3A%20T_2%20%3D%201%20%3A%20%5Csqrt%7B2%7D)
![\boxed {T_2 = \sqrt{2}\ T}](https://tex.z-dn.net/?f=%5Cboxed%20%7BT_2%20%3D%20%5Csqrt%7B2%7D%5C%20T%7D)
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
<h3>Learn more</h3>
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
<h3>Answer details</h3>
Grade: High School
Subject: Physics
Chapter: Elasticity
Hi there!
We can use the equation:
![\large\boxed{{W = F \cdot d}}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%7BW%20%3D%20F%20%5Ccdot%20d%7D%7D)
W = Work (J)
F = Force (N)
d = displacement (m)
We can rearrange to solve for force:
![\large\boxed{F = \frac{W}{d}}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7BF%20%3D%20%5Cfrac%7BW%7D%7Bd%7D%7D)
Plug in the givens:
![F = \frac{150}{1.5} = \boxed{100N}](https://tex.z-dn.net/?f=F%20%3D%20%20%5Cfrac%7B150%7D%7B1.5%7D%20%3D%20%5Cboxed%7B100N%7D)