Wave Mechanics Question 593
Question: The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of oscillation of the bob is $ t _{0} $ in air. Neglecting frictional force of water and given that the density of the bob is $ (4/3)\times 1000kg/m^{3} $ . What relationship between t and $ t _{0} $ is true?
Options:
A) $ t=t _{0} $
B) $ t=t _{0}/2 $
C) $ t=2t _{0} $
D) $ t=4t _{0} $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ t _{0}=2\pi \sqrt{\frac{\ell }{g}} $ . The restoring force in a liquid $ F=-(mg-V{\rho _{e}}g)\sin \theta $
$ =-,( mg-\frac{m}{( \frac{4}{3}\times 1000 )}\times 1000g )( \frac{x}{\ell } ) $
$ or,a=( g-\frac{3g}{4} )( \frac{-x}{\ell } )=\frac{g}{4}( \frac{-x}{\ell } ) $
$ \
Therefore t=2\pi \sqrt{\frac{\ell }{(g/4)}}=2t _{0} $ .
BETA
