A weightless spring of length 60 cm and force constant `200 N m^(-1)` is kept straight and unstretched on a smooth horizontal table and its ends are rigidly fixed. A mass of 0.25 kg is attached at the middle of the spring and is slightly displaced along the length. The time period of the oscillation of the mass is

Options

A. `(pi)/(20)s`
B. `(pi)/(10)s`
C. `(pi)/(5)s`
D. `(pi)/(sqrt(200))s`

Answer

B

Explanation

Given : `k=1000N//m`
When a mass of 0.25 kg is attached at the middle of spring, it will work as the combination of two equal springs in parallel, each of spring constant
`k.=2k=2xx100=200N//m`
The equivalent spring constant is
`k_(eq)=k.+k.=200+200=400N//m`
`therefore` Time period, `T=2pisqrt((M)/(k_(eq)))=2pisqrt((0.25)/(400))=(pi)/(20)s`