The period of a simple pendulum whose bob is hollow metallic sphere is `T`. The period is `T_(1)` when the bob is filled with sand, `T_(2)` where it is filled with mercury and `T_(3)` when it is half filled with mercury Which of the following is true?

Options

A. `T= T_(1) =T_(2) gt T_(3)`
B. `T_(1) =T_(1) =T_(3) gt T`
C. ` T gt T_(3) gt T_(1) =T_(2)`
D. `T= T_(1) =T_(2) lt T_(3)`

Answer

D

Explanation

Time period of penculim doesn't depends upon mass but it depends upon length (distance between point of suspension and cintre of mass). In first three cases length are same so `T= T_(1) =T_(2)` but in last case centre of mass lowers which in turn increaes the length. So in this case time peroid wil be more than the otehr cases.