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Q.

A block of mass 'm' is connected to one end of  a spring of 'spring constant' k. The other end of the spring is fixed to a rigid support. The mass is released slowly so that the total energy of the system is then constituted by only the potential energy, then 'd' is the maximum extension of the spring. Instead, if the mass is releasedsuddenly from the same initial position, the maximum extension of the spring now is  (  g is acceleration due to gravity )

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a

mg/k

b

m g/ 3k

c

2d

d

4d

answer is C.

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Detailed Solution

When it is released slowly it is at equilibrium mg=kd     d=mg/kwhen released  suddenly all loss is potential energy is stored in the form of spring energymgx=12kx2  ; x=2mgk=2d
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A block of mass 'm' is connected to one end of  a spring of 'spring constant' k. The other end of the spring is fixed to a rigid support. The mass is released slowly so that the total energy of the system is then constituted by only the potential energy, then 'd' is the maximum extension of the spring. Instead, if the mass is releasedsuddenly from the same initial position, the maximum extension of the spring now is  (  g is acceleration due to gravity )