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A spring has natural length 40 cm and sp...

A spring has natural length `40 cm` and spring constant `500 N//m`. A block of mass `1 kg` is attached at one end of the spring and other end of the spring is attached to a ceiling. The block is relesed from the position, where the spring has length `45 cm`.

A

the block will perform SHM of amplitude `5cm`

B

the block will have maximum velocity `30 sqrt (5) cm//s`

C

the block will have maximum acceleration `15 m//s^(2)`

D

the minimum elastic potential energy of the spring will be zero

Text Solution

Verified by Experts

The correct Answer is:
B, C, D
`k x_(0) = mg`
`:. x_(0) = (mg)/(k) = (1 xx 10)/(500)`
` = 0.02 m = 2 cm`
So, equilibrium is obtained after an extension of `2 cm` of at a length of `42 cm`. But it is released from a length of `45 cm`.
`:. A = 3cm = 0.03 m`
(b) `v_(max) = omega A = sqrt((k)/(m)) A`
` = (sqrt((500)/(1)))(0.03) = 0.3 sqrt(5) m//s`
`= 30sqrt(5) cm//s`
( c) `a_(max) = omega^(2)A`
`= ((k)/(m))(A) = ((500)/(1))(0.03) = 15 m//s^(2)`
(d) Mean position is at `42 cm` length and amplitude is `3cm`. Hence block oscillates between `45 cm` length and `39 cm`. Natural length `40 cm` lies in betwees these two , where elastic potential energy ` = 0`.
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