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)`

Answer 1

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)`