Three arrangements are shown in figure.

(a) A spring of mass `m` and stiffness `k`
(b) A block of mass `m` attached to massless spring of stiffness `k`
( c) A block of mass `(m)/(2)` attached to a spring of mass `(m)/(2)` and stiffness `k`
If `T_(1)`, `T_(2)` and `T_(3)` represent the period of oscillation in the three cases respectively, then identify the correct relation.

Options

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

Answer

B

Explanation

`T = 2pi sqrt ((m + m_(s)//3)/(k))`(in general)
Here `m_(s)` = mass of spring
and `m` = mass of block.