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A spring of spring constant 200N//m has ...

A spring of spring constant `200N//m` has a block of mass `1kg` hanging at its one end and other end of spring is attached to ceiling of an elevator. The elevator is rising upwards with an acceleration `g//3`. What should be the angular frequency and elongation during the time when the elevator is accelerating?

A

`14.14`rad/s, `0.07`m

B

14 rad/s, `0.1`m

C

`14.14` rad/s, `0.05` m

D

10 rad/s, `0.07`m

Text Solution

Verified by Experts

The correct Answer is:
A
The angular frequency under all circumstance is
`omega=sqrt(((k)/(m)))=sqrt(((200)/(1)))=14.14rad//s`
When elevator is moving up, the equation of motion is
`T-mg=(mg)/(3)rArrT=(4mg)/(3)`
This tension elongates the spring by x
T=kx
`rArr" "x=(4mg)/(3k)=0.07m`
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