question_answer

A cylindrical block of wood (density \[=650\,kg\,{{m}^{-3}}\]), of base area \[30\text{ }c{{m}^{2}}\]and height 54 cm, floats in a liquid of density \[900\text{ }kg{{m}^{-}}^{3}.\]The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length (nearly):                          [JEE MAIN 11-04-2015]

A)  65 cm 

B)       52 cm

C)  39 cm 

D)       26 cm

Correct Answer: C

Solution :

[c] Let block is floating with dissolve depth h.

Then about equilibrium

When block depressed by distance x then

from equation (1)

For simple pendulum

Equating