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A weightless spring of length 60 cm and ...

A weightless spring of length 60 cm and force constant `100" Nm"^(-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 :

A

`(pi)/(20)s`

B

`(pi)/(5)s`

C

`(pi)/(10)s`

D

`(pi)/(sqrt(200))s`.

Text Solution

Verified by Experts

The correct Answer is:
A
When a mass 0.25 kg is attached at middle of spring of constant 100 N/m. Then it will work as a parallel combination of two springs each of constant 200 N/m.
`:. K_(p)=200+200=400" N"//"m"`
`T=2pi sqrt((m)/(k_(p)))=2pi sqrt((0.25)/(400))=(2pi xx5)/(200)=(pi)/(20)` seconds.
Correct choice is (a).
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