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Question
An ideal spring of spring constant k, is suspended from the ceiling of a room and a block of mass M is fastened to its lower end. If the block is released when the spring is un-stretched, then the maximum extension in the spring is ______.
Options
`(4Mg)/k`
`(Mg)/k`
`(2Mg)/k`
`(Mg)/(2k)`
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Solution
An ideal spring of spring constant k, is suspended from the ceiling of a room and a block of mass M is fastened to its lower end. If the block is released when the spring is un-stretched, then the maximum extension in the spring is `bbunderline((2Mg)/k)`.
Explanation:
Let x be the maximum extension of the spring.
From energy conservation,
Loss in gravitational potential energy = Gain in potential energy of spring
`Mg x = 1/2 Kx^2`
`x = ((2 Mg)/k)`
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