One end of an ideal spring of unstreched length `l_(O)=1m`, is fixed on a frictionless horizontal table. The other end has a small disc of mass `0.1 kg` attached to it. The disc is projected with a velocity `upsilon_(0)=11 m//s` perpendicular to the spring.

In the subsequent motion of disc, maximum elongation of spring is `11l_0//10`. the velocity of disc of this instant is:

Options

A. `11m//s`
B. `10 m//s`
C. `5 m//s`
D. `7m//s`

Answer

B

Explanation

Angular momentum of disc about fixed end is conserved, as the spring forces passes througn `O` `m upsilon_(0)l_(0)=m upsilon_(1)((11l_(0))/10),upsilon_(1)=10m//s=(10upsilon_(0))/11`
From conservation of energy we get
`1/2mV_(0)^(2)=1/2mV_(1)^(2)+1/2K_(2)((l_(0))/10)^(2)`
`rArrK_(2)=210 N//m`