Two equal masses are attached to the two ends of a spring of spring constant $k$ . The masses are pulled apart symmetrically to stretch the spring by a length $x$ over its natural length. The work done by the spring on each mass is:

$\frac{1}{2} k x^{2}$

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$- \frac{1}{2} k x^{2}$

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$\frac{1}{4} k x^{2}$

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$- \frac{1}{4} k x^{2}$

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Solution

The correct option is D
$- \frac{1}{4} k x^{2}$

Total work done by spring is $- \frac{1}{2} k x^{2}$ .

Here (- ve) sign because force and displacement are in opposite direction.

Work done on both the blocks is same.
So, work done on each block is $- \frac{1}{4} k x^{2}$

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Two equal masses are attached to the two ends of a spring of spring constant k. The masses are pulled apart symmetrically to stretch the spring by a length x over its natural length. The work done by the spring on each mass is:

The correct option is D −14kx2 Total work done by spring is −12kx2. Here (- ve) sign because force and displacement are in opposite direction. Work done on both the blocks is same. So, work done on each block is −14kx2

Two equal masses are attached to the two ends of a spring of spring constant $k$ . The masses are pulled apart symmetrically to stretch the spring by a length $x$ over its natural length. The work done by the spring on each mass is:

The correct option is D
$- \frac{1}{4} k x^{2}$

Total work done by spring is $- \frac{1}{2} k x^{2}$ .

Here (- ve) sign because force and displacement are in opposite direction.

Work done on both the blocks is same.
So, work done on each block is $- \frac{1}{4} k x^{2}$