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A ball of mass m is attached to the lowe...

A ball of mass `m` is attached to the lower end of a light vertical spring of force constant `K`. The upper end of the spring is fixed. The ball is released from rest with the spring at its normal `(` unstretched `)` length, and comed to rest again after descending through a distance `x`.

A

`x=(mg)/(k)`

B

`x=(2mg)/(k)`

C

the ball will have no acceleration at the position where it has descended through `(x)/(2)`

D

the ball will have an upward acceleration equal to `g` at its lowermost position.

Text Solution

Verified by Experts

The correct Answer is:
B, C, D
initial velocity `=` final velocity = 0 from energy conservation
`mgx-(1)/(2)kx^(2) = 0`
`x=(2mg)/(k)`,
at descended length `=(x)/(2)`
`(kx)/(2)=k. (2mg)/(2k)=mg`
Net force `=0`
`rArr a=0` at lower most position.

force `=Kx-mg=K(2mg)/(K)-mg=mg`
`rArr a=g uarr`
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