As shown in figure a smooth rod is mounted just above a table top `10 kg` collar, which is able to slide on the rod with negligible friction is farstened to a spring whose other end is attached to a pivot at O. The spring has negligible mass, a relaxed length of `10 cm` and a spring constant of `500 N//m` the collar is released from rest at point A. (a) What is its velocity as it passes point B?
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Answer

A, B, D

Explanation

(a) `K_(A) + U_(A) =K_(B) + U_(B)`
`:. 0 + 1/2 xx 500 xx (0.5-0.1)^(2)`
`1/2 xx 10 xx v^(2) + 1/2 xx 500 xx (0.3-0.1)^(2)`
On solving we get
`v=2.45 m//s`
(b) `CO =sqrt((BO)^(2) + (BC)^(2))`
`= sqrt((30)^(2) + (20)^(2))`
`approx 36 cm`
`=0.36 m`
Again applying the equation,
`K_(A) + U_(A) =K_(C ) + U_(C )`
`0 + 1/2 xx 500 xx (0.5-0.1)^(2)`
`=1/2 xx 10 xx v^(2) + 1/2 xx 500(0.36-0.1)^(2)`
On solving, we get
`v=2.15 m//s`.