A pan with a set of weights is attached to a light spring. The period of vertical oscillations is `0.5s`. When some additional weights are put in pan, the period of oscillations increases by `0.1s`. The extension caused by the additional weights is

Options

A. `1.3cm`
B. `2.7cm`
C. `3.8cm`
D. `5.5cm`

Answer

B

Explanation

`T=2pisqrt(m/k)implies0.5=2pisqrt(m/k)`
`(1)/(4pi)=sqrt(m/k)impliesm/k=(1)/(16pi^2)`
`T+0.1=2pisqrt((m+m^')/(k))`
`0.5+0.1=2pisqrt((m+m^')/(k))`
`((0.6)^2)/(4pi^2)=(m+m^')/(k)=m/k+m^'/k=(1)/(16pi^2)+(m^')/(k)`
`m^'/k=((0.6)^2)/(4pi^2)-(1)/(16pi^2)=(1.44-1)/(16pi^2)=(0.44)/(16pi^2)`
`m^'g=kximpliesx=m^'/kg=(0.44)/(16pi^2)g`
`=2.7xx10^-2m=2.7cm`