An ideal spring with spring constant is hung from the ceiling and a block of mass is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is:
Explanation for correct option
Step 1: Given
Step 2: Formula used
Step 3: Find the maximum extension
The spring constant is .
A block of mass is attached to the spring, which is attached to the ceiling.
The spring will stretch because of the weight of the block.
Let the weight at the spring's end cause it to be stretched by a distance from its equilibrium position.
The block has a mass of .
Since there is no longer any external force acting on the spring, it will now be stretched with a force of .
By compressing to the equilibrium point, the spring will make an effort to keep its original shape.
The spring will experience a restorative force of,
Where is the spring constant
The energy stored in the string is
The potential energy stored in the block is,
The energy stored in the spring must be equal to the potential energy of the block.
Hence option B is correct