question_answer

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 to in air. Neglecting frictional force of water and given that the density of the bob is\[(4/3)\times 1000\]\[kg/{{m}^{3}}\]. What relationship between t and\[{{t}_{0}}\]is true?                                      [AIEEE 2004]

A)  \[t={{t}_{0}}\]

B)       \[t={{t}_{0}}/2\]

C)  \[t=2{{t}_{0}}\]          

D)       \[t=4{{t}_{0}}\]

Correct Answer: C

Solution :

[c] The time period of simple pendulum in air

.(i)

being the length of simple pendulum.

In water, effective weight of bob

weight of bob in air – upthrust

wheredensity of bob,

density of water.

..(ii)

Thus,

[dividing Eq. (ii) by Eq. (i)]