Answer:
f' = 2 f
Explanation:
The frequency of the pendulum that swings in simple harmonic motion is given by :
[tex]f={2\pi}\sqrt{\dfrac{l}{g}}[/tex]
Where
l is the length of pendulum
g is the acceleration due to gravity
If the length of the thread is increased by a factor of 4, such that, l' = 4 l, let f' is the new frequency such that,
[tex]f'={2\pi}\sqrt{\dfrac{l' }{g}}[/tex]
[tex]f'={2\pi}\sqrt{\dfrac{4l}{g}}[/tex]
[tex]f'=2\times {2\pi}\sqrt{\dfrac{l}{g}}[/tex]
f' = 2 f
So, the new frequency of the pendulum will become 2 time of initial frequency. Hence, the correct option is (b) "2f"
