The time period of a simple pendulum whose bob is a hollow sphere is `T`. The period is `T_(1)` where 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 pendulum does not upon mass but it depend upon length (distance between point of suspension and center of mass). in first three cases length are same as `T = T_(1) =T_(2)` and in case center of mass lower which in furm increase the length. So in this case time period will be more than the other cases.