Finding the Max Extension of a Spring

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To find the maximum extension of a spring with spring constant 'k' when a mass 'M' is attached, apply the principle of energy conservation. Initially, the gravitational potential energy of the mass is converted into elastic potential energy of the spring at maximum extension. The equation used is Mgh = (1/2)kx^2, where h is the maximum extension and g is the acceleration due to gravity. Rearranging gives x = sqrt((2Mg)/k) as the formula for maximum extension. This approach ensures the correct application of energy conservation principles in solving the problem.
rgujju
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An ideal spring with spring constant 'k' is hung from the ceiling and a block of mass 'M' is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is?

Please tell how to do it and the final answer.
 
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Consider energy conservation.
 
I tried but i am not getting the right answer..
 
Show what you have tried. You are required to by the rules of the forum.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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